Crossdressing used to be a big mainstream thing in Japan prior to the world wars (the government wanted men to want to be soldiers, and that doesn't work so well when everyone wants to be a little girl), but since then its only resurrection has come about recently as a part of otaku culture. Even then, its only really for young adults, rather than actual adults, which Amane looks like. Of course, the idea of a 'man' is more feminine in Japan, since the big bulky Zangiefs are considered the homosexual ones, but it doesn't go that far. I'd say the best example of it is probably Dante, who, while I don't think you'd find anyone who'd say Dante isn't manly in the West, is pretty close to being a bit of a poof.
So yeah, while being a beautiful man who crossdresses isn't really unheard of, its not a mainstream thing, so I think he's fine under the 'trap' label, though of course he's closer to the edge with Ash than in the direct centre with Bridget.