CMT here also. It can cause hand issues similar to what you describe, I am experiencing them myself. Like you I don't have access to my family history, but my eldest son has it as well, which pretty much confirms my diagnosis.
I am with Kitt on questioning the value of the testing, but you can come to a pretty definitive diagnosis between symptoms and neurological consult.
My toes also go through the spasms where they move on their own. I can no longer move the middle toes on my left foot at all, all the others only move slightly and it causes pain and spasms to try. My hands are starting to do the same thing.
I think that you have enough symptoms to at least suspect it. One of the things that distinguishes CMT from idiopathic neuropathy is muscle wastage and weakness.