Queen to E6 i think
Interesting Puzzle!
Creative!
It requires understanding the "order of worseness" Worst are the black mates which are "unavoidable" after the first move even when both sides don't want it! Hunky's solution is in the 2nd category which enables white to force mate with his best play.

After move 1, black is automatically mated in one of three ways. Either Be6, Bd5, or e6, depending on White's 2nd move and Black's 3rd. So black can either mate White in one move with Qf5, or mate himself with another! If you remove even one of his pieces, it won't work.
As for Qe6, as arisktotle said, white doesn't have to recapture, or he can just take with his rook, so the game still goes on at least for White's move.
This is definitely the most fascinating puzzle I've crafted due to the beauty of the the various pins, and how pinned pieces (which can still capture a king) pin others, so forcing the desired moves.

I actually very much wanted to place a white queen on the square black is supposed to move to, (and say 'if you take his queen, it's game over, and also hiding the tactics,) but I realized that doing so would make the position impossible to reach from the starting board, since black must have made 4 captures, and changing his position would ruin the puzzle.
It's an excellent composition! Nothing wrong with the stipulation "worst move" as it will make solvers ponder on that scale of worseness. From the assumption it is sufficiently intuitive to give everyone a fair chance!
I made a worst move problem based on an e.p. capture. This is commonly not allowed (unless provable) but it is arguable that "the worst move type" can be interpreted as "worst move in the worst possible game history"!
I actually very much wanted to place a white queen on the square black is supposed to move to, (and say 'if you take his queen, it's game over .......,
That's the sort paradoxicality that commonly works for compositions but not here. With or without a white queen, white already has the checkmate threat of category II on e6 and needs no extra queens. With one, we must be looking for "worst moves" of category I where white pieces are as much a threat as an aid to accomplishing blacks selfmate. Just to say that I prefer the unoccupied eye in the storm as it is now! It would be different if the white queen would play a role in thematic black tries in the diagram, e.g. by blocking an escape square for the white king.
It's Black's turn! Can you find the worst move?
I specifically made sure it's a position that can be reached from the starting board!