When something is being seen, is it a direct object (Accusative)?
Widzę kogo co (Accusative)
Nie widzę kogo czego (Genitive)
It just happens that plural masculine personal (mężczyźni) and singular masculine animated (mężczyzna) have Accusative and Genitive forms the same
Can I say I see no man?
Not really. Firstly, it changes plural to singular, and secondly, it sounds more like 'żadnego mężczyzny' even than just 'mężczyzny'.
Sorry. I meant I see no men
Then this seems acceptable, even though 'żadnych mężczyzn' would be closer. Added now.