Are you aware that knapping stones works slightly differently than knapping flint?
When you place a piece of flint, you instantly see choices for knapping. However with stone, you place a piece of stone and it just sits there. You have to act as though you are placing it again to see the choices for knapping. I suspect this may be the problem you're having, since you say that you "can only knap flint."
Regarding rebinding the keys: I think you already know this, that when you rebound Crouch to Ctrl (instead of Shift) it changed knapping to Ctrl right click. If you can actually knap flint using Ctrl right click, then I think the issue is what I wrote above.