I don’t know if this helps at all but neowalksticks has some amazing canes that you can customize, a little pricey but amazing!

Could be a silly question, but is the handle padded or hard? It could be a simple as perhaps you need more padding on the handle. Or perhaps it's the material itself that the handle is made out of, and it's creating friction with your skin. If you could find a fabric that is more gentle on your skin, or that prevents the rubbing, you could fashion a sort of cap for your cane out of that. Don't know if any of that's helpful, but I'll continue to see if I can think of anything, and I'll be sure to let you know if I do.

I sometimes use hiking sticks.