I've got a weird toe that causes me pain. What are the chances a doctor would amputate?

Hey docs,

Because of another neurological condition (Charcot Marie Tooth), I have some weird feet. One of those weird thing is that my fourth toe is really long, and because of the CMT hammer toes, it curls in and I find it hitting the ground actually on the nail, or stepping on it with my third toe. It's always callused. Walking on hardwood or cement floors is torture. It super sucks! It hurts a lot! I use orthotics and they help with other things, but not this.

What are the chances that, if I went to a doctor and said 'hey, I want to shorten this toe', they'd think it's a good idea? I can't seem to find any information on whether fourth toe amputation would affect my gait (any more than it already is from 1) CMT, and 2) the pain of walking on the toe).

I'm an otherwise healthy 31yo female, with access to sweet, sweet socialized medicine.