First of all, congratulations, hon. I truly believe that life is too short to play by someone else’s rules. You just have to be who you are. My own biggest fear is being on my death-bed and realizing that I never took a chance to do (or be) something really important to me because I was too scared, and I vowed that I’m never going to let that happen to me.
I’m male, but as you can see by my pic, I do favour a pretty androgynous/feminine look myself. It’s taken me a while to be comfortable being open about it, but I took the plunge about eight years ago and honestly, I’ve never been happier. My friends, family and neighbors are all supportive, and I live in a rather progressive town; I’ve never had a bad experience being out and about (pun intended

) so I guess I’m pretty lucky.
My suggestion to you would be to simply ask around in a few local salons. Be up-front about what you’re after, and see what sort of response you get. If you act self-confident (but not belligerent, of course) people will usually respond positively to that. A “this is how I am, and I’m fine with it” attitude will encourage others to respond in kind, I’ve found.
I suppose there will be a few who may respond badly (although probably far less than you’d think), and you just have to be ready for that. Generally, most shops and salons have the attitude that your money is as good as anyone else’s, and if they can help you out, then it’s win-win: you get what you want, and they get paid. My own experience has been that many girls in hair and aesthetics salons (and clothing, cosmetics and jewellery stores too, for that matter) are actually pretty enthusiastic about helping a guy look more feminine. Don’t ask me why. Maybe it has something to do with finding something in common (hair, makeup, nails, jewellery, whatever) that they can share… in other words, the guy expressing an interest in being on the same “team” so to speak. (And by the way... yes, as you say, a few people will definitely think it's weird, but my experience has been that it's far fewer people than you'd expect.)
So, do give it a shot! There are short feminine hairstyles, even ones as short as a couple of inches, although I would definitely encourage you to let it grow, if you can, since that would open up a lot more possibilities.
And best of luck! (sorry about the long-winded reply)
Time flies like an arrow. Fruit flies like a banana.