Specifically, I would like to know whether it was before or after the movie in which he did not have a mouth.
1 Answer
The first reference I can find is from Deadpool: Sins of the Past Vol 1 Issue 1 that was released August 1994. Incidentally this is also the reference to the nickname from the Fandom page for Wade. The name appears as a caption not said by a character as far as I can tell.