Perhaps he'd be more appropriate as a mod for a Donkey Simulator but, alas, that does not exist. So here is Shrek, as a skin for the open-world rampage that is Goat Simulator.
The game is largely broken with a quadripedal Shrek, though players still can unleash all the mayhem that they can in the original game. If the video looks stupid, well, the game is intentionally stupid. A Shrek mod simply contributes further to that goal.
If, for some reason, you want this mod, it can be downloaded here.