If instead of using a food processor or blender, you hand-chop and mash the finely chopped coconut meat in cheesecloth, you can still follow most of the many recipes online. For a very small investment, you could purchase a grater to make it a little easier.
Here are some instructions including a grater approach which seems adaptable to a knife-and-elbow-grease approach. Here's another, similar set of instructions for comparison.
You said in a comment that you were concerned with yield and waste. She says she gets about 200mL oil from three coconuts. But I suspect that's using her electric gadgets and that you may not see quite that yield using a knife and/or grater.
You'll be left with mashed coconut pulp. This can be dried and used to cook with. Get it pretty fine and it’s basically coconut flour. A lot of people (esp. those who are restricted to low-carbohydrate intake and have to avoid grains and many other starches) use coconut flour in breads and pastries and as a thickener. (I believe it's considered low-FODMAP in moderate quantities.)
This site shows one cup (80 grams) of shredded coconut has 12.2g of total carbohydrates, 7.2g of which are indigestible fiber. The sugar content is quite low at 5g, less than a third of which is fructose. I do not think that can be reduced, but I consider that a good fiber-to-sugar ratio.