This should not be plural, should it? "There are no men here" is plural. this is Genitive and so "no Man"... I do not thing "there are no men here" should be accepted.
It's not an exact translation in terms of grammar, but frankly, "There are no men here" would most probably be translated the same way.
I'd only say "Nie ma tu żadnych mężczyzn" in plural if someone explicitly mentioned that they're searching for men and they expect those men to be here.