I think that "Ten mężczyzna czyści basen" would be more accurate, but both sentences are correct.
It probably isn't a good translation here, but could "sprząta" mean "he tidies" in another context?
Yes, it could.
Pool cleaner? Ah, the jokes almost write themselves...
My answer was wrong because i didnt put "swimming" in front of "pool". I think most people would assume "pool" means the kind for swimming without the extra word (as opposed to a pool of blood or something).
Just 'pool' is accepted already.