KN vs KP Endgame Draw or Win for White?

Hi, I was wondering if a King and Knight against a King and Pawn is won for white assuming black runs out of time, as it is possible to checkmate with a King and Knight against a King and Pawn. If a timeout happens, we assume the player that timed out plays the worst moves after the timeout. 

Here's an example of a KN checkmate for white against a timed out KP black player.

Also, here's a position where white can checkmate even though the black pawn is not on the h or a-file

In both positions, we assumed that black played the worst moves possible as he timed out already, and it's proven that checkmate for white is possible. Is the result of these positions draws or wins for white, if black times out?

Wins