Plus "trap", just on its face, isn't a 1:1 for transwhateveryoumay anyway. Some trans people find it offensive, hear it and think that it's some sort of sexual predator casting where they're being thought of as "traps" for straight guys to get "caught" in when it's really just a silly reference to the old Admiral Ackbar meme from the aughts. It originally came about as Western people were being exposed to otoko no ko art (which is a goofy pun that refers to boys being drawn as very feminine to the point of being mistaken for girls or possibly crossdressing as girls) and would then make the same dumb joke over and over until everyone actually started calling them traps - and from there, like reverse harems before it (personally I find "reverse" to be a completely unnecessary and kind of a confusing distinction to those who don't already know, but that's what people use), reverse traps referred to girls drawn more masculine or crossdressing as boys.
There's some element of taking others by surprise inherent to the character type so trap actually ended up fitting in a roundabout and perfectly silly way. The important thing to note that those who weren't aware of the origins of the word might not know is that it's not actually connected to transgenderism. In fact traps and reverse traps often think of themselves as boys/girls but, either reluctantly or willingly, end up looking cute or tough against the typical expected presentation for boys or girls. It doesn't even -have- to incorporate crossdressing necessarily though that is quite common.
A trap, whether the boy or girl kind, could certainly -be- transgendered but they're not actually the same thing. It's more rooted in androgyny and challenges some "this or that" gender norms in the perception of others and how the characters perceive their own masculinity and femininity. So keep in mind that it's primarily a term for a type of fictional character and a pop culture word with porny roots. In a game like this trap is more than appropriate - but def. don't go slinging that one around everywhere when it comes to describing real people.