It's a persona, not a lie. Though it could likely lead to lies (if e.g. his employer or somebody else starts asking him intrusive questions).

But even then, how do we draw the line between "lying" and what might be considered cosplay? He is basically playing the role of a transexual, for a good end. And to play the role well, he must act and speak in character. Neither roleplaying nor his intentions are evil. So it would seem even if he outright said "I am a transexual" then he wouldn't be lying, any more than Christian Bale would not be lying even if he outright said "I am Bruce Wayne" while playing the role of Bruce Wayne.

But I probably wouldn't do it. I can't say whether there's any sin, but I wouldn't want to risk it. Not only is there a potential issue with what might be lying, but there's also a potential issue with what might be crossdressing.

Re: OP

I don't believe in "gender"

You don't believe in gender in the way the pro-trans people interpret it, or don't believe in gender period? You should believe in gender. The pro-trans people are wrong in believing that one's sex is unrelated to and seperable from one's gender, but gender is nevertheless real.