Yes, anesthesia is one of my main concerns.

I'll definitely be questioning the vet if the procedure has to be done.
I think I'll try the gauze, LuvMySissy. I've tried a fingerbrush without success so this sounds like a good way to do it. I'll also look into the products you mentioned. (When I read "alcohol" and "arsenic" in the ingredients list I kind of had a

moment, but I know some people here use those products so I wanted some feedback.)
Again, thanks everyone!