I actually happen to know the answer to this one as well , but I don't have the moves to back it up.
shortest game not mate by white

I do want the moves to back it up. But if you say the number of moves I'll say you are right (No more than 3 guesses or answers without backing it up!)
I think the answer is 5 (total moves) with checkmate by black. this seems too simple so there must be a catch. i can back this up with moves.
This is similar to my last question.
Excluding ckeckmate given by white, what is the shortest game possible? This excludes games where players resign or agree a draw. For example if a player resigns on move 2 or both players agree a draw on move 2 this would not be included. The shortest game is the minimal number of moves.
If no one gives the answer by tomorrow (with the reason) I’ll give a clue tomorrow, and give the answer on Friday.