I'm with the lady. A decent wallet has plenty of space in it. I never was a fan of huge wallets, so I've always had a small tri fold one. It wasnt a "male" wallet, but it was nondescript. my grandmother bought it for me when i was still in high school. My old wallet broke (the leather was very old)and I really need to replace it, but I've been using a business card holder for a while now. I carry mine in a front pocket or in my suit jacket, though I'm out of suits for the time being since they were old.
I will say that in Japan everyone, male or female, has those huge honking ones and they just have then dangled precariously in their back pockets. I do carry a small shoulder bag though, which is very common here and back in Alaska amoung younger people. Messenger bags don't look out of place.