"We are men."
Well, technically it's not the best thing to think about it as "the second z", because it's a separate letter. Both ż and ź are. If the alphabet developed differently, it could use a completely different signs for these sounds ;)
Anyway, you can find the declension of "mężczyzna" here: https://en.wiktionary.org/wiki/m%C4%99%C5%BCczyzna#Declension - only a few forms have this softening of z to ź.