Hypothetically speaking,

Probably by articulating their moves with someone to help them move.

Not to say that I will ever be good enough to participate in a tournament, but I'm just wondering if such occurrence has been recorded...

They could just say the coordinates and either their opponent or a helper moves the pieces. Touch rule could apply to them speaking, etc. I'm sure a solution could be found that is within the spirit of the rules and maintains fair play.

There are guidelines on how to assist players with disabilities. Accommodations could vary between different tournaments.

I played a blind guy in an OTB tournament once. That's a lot harder than having no hands. For us the TD (tournament director) made accommodations like people have said.

For the blind player, obviously I had to announce my move to him verbally... I assume someone who had no hands (or let's say, no arms) would simply announce his move to his opponent, and his opponent would make the move on the board.

Pretty easy.

right now, I click with my note