The short answer for your substitution question is -- add some baking soda, i.e., sodium bicarbonate.
How much? I don't know, as the recipe doesn't even give a hint. Start out with a little -- maybe a half-teaspoon? You can always add more, but it can give an unpleasant aftertaste. With a little bit of baking soda, producing an alkaline solution, the okra will get a bit more green and the meat may be slightly tenderized. As you increase the concentration of baking soda, the okra will likely get mushy and "slimy." Baking soda often is described as giving a "soapy" consistency to food when used in excess.
As to the bit about "saltpetre," it's almost certainly a mistranslation (apparently a very common one in West Africa).
This was quite an interesting business to sort out. I'm no expert in the cuisine of Ghana or West Africa, so if anything I will say here looks wrong to someone with first-hand knowledge, please correct me.
If you care about the logic and sources I'm using to justify all of this, details are below.
My guess is that the confusion came out of the fact that these West African salts are often known in English as "potash." Another traditional name for "saltpetre" is "nitrate of potash," which would be the old name for potassium nitrate (itself often a component of "potash" when used as fertilizer). While these salts are very common in West Africa and are known in English as either "potash" or "saltpetre," the largest composition is generally sodium (bi)carbonate and/or potassium (bi)carbonate. There's no potassium nitrate involved at all. As you rightly identified, potassium nitrate is a curing salt, which needs to be used in precise quantities, generally to preserve meat.
Potassium nitrate, however, is NOT generally known for making vegetables "slimy," nor (as the Wikipedia page claims) for reducing bean cooking time or to soften tough meat. I was suspicious of the Wikipedia claim and tracked it back to its first appearance in the article in 2012, and it's never really been properly sourced. A quick search of Google Books demonstrates that most of these claims similar to Wikipedia only appear in books and sources since 2012, probably imitating the Wikipedia article.
(I'm sure I've gone on about this before, but never believe anything on Wikipedia unless you've followed the sources and verified. It's a great resource, but information must be verified and properly sourced, as anyone can edit it.)
Furthermore, an alkaline tenderizing agent like sodium (and/or potassium) carbonate or bicarbonate immediately occurred to me as better fitting the culinary description from Wikipedia. For example, baking soda is well-known to speed the cooking of beans.
Anyhow, what we're really talking about here is a "salt" that is used in West Africa, which is not sodium chloride. It goes under a lot of different regional names: kanwe, kanwa, akanwu, kuan, natron, trona, nikkih, kilbu, sel gemme, and limestone are a few, in addition to potash and (quite inaccurately) saltpetre. Traditionally, it is often a harvested "salt" from regional lake deposits, but there are a variety of other preparations and methods for making it, depending on the country/region.
So, how do I know the Wikipedia article is wrong and what is requested in this recipe? Well, first let's begin with a study done in Ghana itself by USAID, which mentions this specific dish on page 38:
Fresh okro soup: Prepared similar to light soup but with added chopped
boiled okro with kanwe (saltpeter).
Here we have confirmation that the local name for this salt is "kanwe," but it is also referenced as "saltpeter."
Later in this study (p. 167), we are told that "saltpeter" is "kanwa" and that it speeds up the cooking of beans (just as the Wikipedia article tells us).
Beans are an important part of the IYC diet and mothers use
sal[t]petre (kanwa) to speed the cooking process. It is not known
whether saltpeter has any adverse health effects and this needs to be
investigated.
So, we're looking for kanwa/kanwe. And aside from Wikipedia and a few sources that seem to mimic that source since 2012, I haven't found any sources that connect this to potassium nitrate. Most commonly, despite the misnomer of "saltpetre," academia studies that have analyzed such salts have found they contain "potash" instead, or potassium (bi)carbonate.
(Technical note: the carbonates of sodium and potassium have similar chemical properties to the bicarbonates but are stronger, i.e., have a more alkaline effect. They'll also do similar things to food.)
For confirmation of what "kanwa" is, we can look to this article:
Sariem et al., “Acute toxicity studies and characterisation of local dietary salts in Nigeria” (2016)
Local dietary salts in various forms are used in Nigeria as food
seasoning and food additives. Potash is commonly consumed in Nigeria
especially in the northern parts where two forms are commonly
available: kanwa and shem. Kanwa, also known as natron, a
sesquicarbonate or hydrated carbonate of sodium (Alawa et al., 2012).
Kanwa is also known scientifically as trona (Omajali et al., 2010).
Okehie-Offoha in 1996 however described kanwa as a potassium salt in
combination with other salts. Kanwa is a base with a pH of 8.9. It
contains 10% sodium as bicarbonates, 70% potassium, 0.33% calcium and
8% phosphorous (Yakasai et al., 2004).
[…]
Kanwa is used to soften food and reduce cooking time when boiling
beans and tough meat. Kanwa is also an essential ingredient in making
special porridges such as kunun kanwa literally translated from the
Hausa language as 'saltpetre porridge' (Okehie-Offoha, 1996).
I'm just going to note this last bit is very similar to the sentence following the quotation from the Wikipedia article given in the question, which states:
It is also used to soften food and reduce cooking time when boiling beans and tough meat. Saltpetre is also an essential ingredient in making special porridges,
such as kunun kanwa literally translated from the Hausa language as
"saltpetre porridge".
Both of these cite the same source. I'd like to believe Sariem et al. actually went and found this source and verified what it said. But it unfortunately looks like they may have simply plagiarized a couple sentences from Wikipedia here, as this passage has been on Wikipedia since 2012, and their article didn't appear until 4 years later.
(Again, a warning about the dangers of Wikipedia. Even scholars overuse it without checking.)
Yet, as we know from the USAID report above, "kanwa" is apparently sometimes known as "saltpeter," even though as discussed in the Sariem et al. quotation above, we also know it's more correctly a form of potash, i.e., a potassium bicarbonate salt, along with sodium bicarbonate and some other minor components. ("Sesquicarbonate" and "hydrated carbonated" are synonyms for "bicarbonate.")
Sariem et al. is useful for summarizing a bit of the literature on the composition of kanwa. One final source I'll bring into the mix points out the regional variability of these salts:
Ngoualem et al., “Variability and Functionalities of Salts Used in Traditional African Food Preparations“ (2019)
Common edible salt, a natural evaporite which can be obtained from
sea, underground ore or natural brine, and containing at least 97% of
sodium chloride (NaCl), is the main salt used in food preparations,
with the only objective to improve the taste of foods. Out of that,
other specific salts which have been reported to be used in food
preparations are Lakes’ deposits, plant-based ashes, their filtrates
and evaporites of these filtrates. Their chemical composition shows
that they are mixture of salts and thus, made of cations and anions,
major cation being generally sodium or potassium whereas major anions are generally carbonates, bicarbonates, sulfates and
chlorides. Their usages have mostly been reported in African
countries (Nigeria, Niger, Chad, Cameroon, Ghana, Kenya, Burkina
Faso, Uganda, Tanzania, Sudan, Central and East African countries)
[…].
In Africa, they have been reported to be used to reduce the cooking
time of legumes, vegetables and cereals, to improve the green color of
vegetables as well as to increase the viscosity of sticky ones, as
emulsifier, and as flavor enhancers. These functionalities have been
attributed to the alkalinity of their aqueous solutions. Since the
solutions of Traditional Salts are alkaline, they can also be named
Traditional Alkaline Salts (TAS).
To summarize the important bits from this last quotation:
- We might have various mixtures in these salts of sodium and potassium compounds, namely carbonates, bicarbonates, sulfates, and chlorides. Note, however, the conspicuous absence of nitrates. There's no potassium nitrate here.
- These salts are found in Ghana (as well as many other places).
- They are used to have the effects both listed in Wikipedia (incorrectly attributed to saltpeter/potassium nitrate) and in the recipe. They reduce cooking time of legumes, and they increase the viscosity of sticky ones (hence, I suppose, the "slime").
- The main aspect that makes these salts useful in cooking is their alkalinity in solution.
Hence, I finally arrive again at my initial recommendation: you need an alkaline solution. The most common item found in kitchens that will give you an approximation for this recipe is sodium bicarbonate, i.e., baking soda.
Lastly, I will note that the composition of these salts appears to vary significantly by region in Africa, but potassium (bi)carbonate seems to often be the most prominent ingredient, hence the alternative English name of "potash" for these salts. If you wanted a more authentic option, you could do an internet search for "kanwa" and find all sorts of interesting crystals people are selling. Or (if you're less adventurous) you could perhaps buy some pure potassium bicarbonate, then mix in a smaller proportion of baking soda, and you'll be most of the way there to something similar to the traditional West African culinary salts.
That said, I don't really think the important part here is the flavor from the salt, other than maybe some trace minerals (which likely vary significantly by source/region). Thus, baking soda will probably do in a pinch, and hopefully give you some nice slimy okra.