The smallest outboard will do the trick, however,
this assumes you're not pushing against wind or current. Given no other forces you could theoretically push your 37 along with just two fingers, however, those two fingers would take quite a while to get it moving and then stopped again (it's that old high school physics mass/force/time thing.)To answer your question though, a 2 horse outboard will get you into your slip in a pinch but you'll find that it's more about technique than power. If you're short handed a hip tow provides nice control of the mother ship except that you may not be able get into your slip with that arrangement. At that point anchoring off and coordinating plans with someone in the dinghy who is good at maneuvering and helping hands at the slip will get you in without too much drama. As with normal docking it's more about techenique , planning and communication than brute force.