Mmmm, it's a hard one cause we don't like turning way business but you MUST look after yourself first.
We live in a very diverse world these days and men are doing things now they have never done before, so it could be a legit thing.
Maybe he's going to a dress up party and there's a big prize for the best dressed and he wants to go all out, maybe he is a cross dresser and if so, then that's his business, not ours and maybe he is a sicko and wanting to cause problems.
So with all these different variables in mind, I would try and talk to him via phone to get more of an idea of what type of person he is and what he wants.
I don't see why you couldn't outright ask why he's wanting them and you might be shocked as to his answer (in a good way) and you could just nicely say to him that it is a odd and rare request and this is why you are asking and depending on what he's like on the phone and his answers, you will have to make your mind up from there.
Also during this call you should let him think that you do NOT work alone, that you have someone else around in the back of the house/salon.
But foremost, use your gut instinct, never ignore your gut in this type of situation. if during or after you actually speak with him and your gut feels yuck about it, listen to it and put him off by telling him you are fully booked in all the time slots he is asking for.
But honestly, if it's just a matter of an innocent reason (like a dress up party, a dare or a simple cross dresser) then I wouldn't say no and let my own personal judgement against odd/different people stand in the way. For instance HIS cross dressing does not have any affect on you apart from helping to line your hip pocket, which is a positive thing. Is you have to do is, do his toenails and gt paid and send him on his way. He might end up being a regular if he's all legit and not a creepo
Good luck.