Then it's checkmate, not stalemate. For a stalemate you need a situation where the king is not in check, but there are no legal moves. It seems impossible in practice, if not in theory.
A queen and a rook or bishop also can enclose a triangular area that is just large enough to contain the king.
(Talking of bishops: should this game require bishops to stay on squares of their starting colour?)
Given how captured work and how you'd probably define "on a square" with white a bit of freedom (perhaps the center of the piece has to be within the square?) I doubt it'd matter much either way.