What can I replace oversized waterproof outlet cover with?
Easy. Just get a round to single gang adapter like this:

Amazon even suggests this is bought together with an in-use cover and GFCI, so you are clearly not the only one with this problem.
If you don't have GFCI on this circuit, you should add it. Even with an in-use cover, that would be better done inside (breaker panel or an earlier receptacle in the circuit).