A company shouldn't be doing anything to you based on an extra curricular, as it were (non-company related activity, you get what I mean). Just like, although the CEO might not like, say, square-dancing, he has no way to do anything that would actively affect your job position based solely on the fact that you go to a square-dancing club after work (just one really terrible example).

If you are worried more about your coworker's finding out, there seems to be a simple solution; don't let them see you do it.

If you actually want to do it at work; there isn't really a way to get around this one. Your job might not be in trouble, but the social situation of your position might go down because of how you dressed. I can get that. However, I would ask myself first, why exactly do you feel like you need to wear a dress to work? Is it because you like wearing dresses, or because you want to prove something to yourself, that you aren't fully assimilated? Why, precisely, would wearing a dress accomplish this better than say, protesting for LGBT rights, or working with the homeless, or something like that? What, precisely, does cross-dressing get you that you can't find elsewhere? Is it the thrill that you seem to be associating with it? If yes, then that is sort of the point. If you want to feel a thrill, there has to be some sort of implicit danger involved; if there were none, you wouldn't really be feeling anything.

I for one, happen to like suits; I like wearing them, I like to see men wear them. I generally prefer them to women's clothing (although I did cross dress in preschool; also, my parents are AMAZING. Like, I went through all of preschool wearing a dress every day, and never got any flak for it, from anyone. I don't remember a single person ever saying that only girls wore dresses, or that I was being "wrong". I am so glad my parents are so awesome). I don't like to wear women's clothing at all though, so maybe it is just me.