During a dental on a cat or dog the wow bandage tied to the et tube gets all minging,

Why dont you try a used drip line to tie in the et tube. It's easily washed down during the dental, it does not catch.

Instead of using gloves to keep foot bandages dry try using an old drip bag. Cut the bottom of the drip bag off and cut a few slits around the top of the bag to thread a bit of bandage through and tie it around the animal's leg.