After researching this, I think there are a few possibly options you could try (though I haven't personally tried any of them, they seem worth experimenting with).
Apparently isomalt can be used in place of sugar in most cotton candy machines - though it should be ground and sifted so it doesn't damage your machine. Isomalt may be a better starting point than sugar to get you in the direction of savoury, as it has only 50-60% of the sweetening power of sugar.
This is an interesting chemical that interferes with your tastebuds and inhibits sweet flavours (it blocks the TAS1R3 sweet protein receptor). Apparently adding this at a concentration of 100 parts per million will block sweet flavours. In that same link it discusses Domino's Pizza using this so they could add sugar to their pizza crust for aesthetic reasons - to encourage browning while it baked, but inhibit the sweet flavour as obviously that isn't what most people are after in a pizza.
There seems to be a few ways people do this. The easiest option seems to be flavouring the isomalt or sugar using flavour extracts or essences. A quick google search seemed to indicate that pork essences/extracts exist, so this could be an option if you're after ham. One important note I saw in a few places was if it is a liquid essence, add slowly to prevent clumping, and ensure it is completely dry before attempting to use it. If you're adding a flavour that naturally has a lot of umami flavour, you could also try adding some MSG to bring this out even further.
Another approach to flavouring the isomalt/sugar seem to be simply mixing the sugar with other ingredients and letting it infuse over an extended period of time (this seems to work with things with strong flavours, e.g. herbs, spices, coffee beans, chillies, fruits, and other whole ingredients). You could also try blending more delicate ingredients directly into the sugar directly (those approaches are described here).
Though I don't have any references to support it, I have seen some discussion of further enhancing the flavour of infused sugar by heating the infused sugar to hard crack stage (146 to 154 °C, or 295 to 309 °F), then breaking this back down into a powder. I'm not sure if this does work, or how it would work with isomalt, but another potential experiment to try.
A quick warning: All of the suggestions I've given should work in a cotton candy machine in theory. In researching this I spotted a lot of discussion of different ingredients burning/damaging machines cotton candy machines in some way, but couldn't spot a consistent pattern of what caused this damage and what didn't. You might have to take a risk if you want to experiment enough! I'd love to hear your results if you do try it.