Ow, that must be damn painful, the quicker he sees a vet the better. Anything you might wrap it in would be reduced to threads, although those elastic bandages that you can get at the dollar store might work. I think it will probably take at least two people to carry out this operation
; they might protect him for a few hours, depending on whether or not he objects.
Docking sounds like the best solution but the vet will tell you. Have you asked him about a payment plan, so you can take the cat in sooner?
You are so kind to watch over this guy, he has obviously crept into your hearts!