Transvestite is a good word. Used for over 100 years: “person who wears clothes designed for the opposite sex”
There’s a difference - in history, those referred to as “transvestite” trans-crossing + vest - to wear/apparel. To appear the opposite gender... essentially ended at the living out of the fantasy in particular settings.
There are still “transvestites” -some of which have no problem identifying as such. Popular reprobates of that ilk would include RuPaul - who doesn’t claim to be a woman - only that he enjoys dressing as such (though he also is a homosexual).
The entire “transgender” garbage is an entirely different bird - it is where these people have convinced themselves that they are actually the opposite gender (or of no gender at all). It’s more than a fantasy roll-play game. It is a full-blown fraud perpetrated on themselves and the world around them.