I just started wearing fedoras last summer after a dermatologist read me the riot act (while removing a small bit of "pre-cancerous" temple). But in reality, that just gave me the excuse to do something I'd wanted to do for a long time.
Since I teach at a college, I was able to wear some cheap (and I do mean cheap) straw fedoras during the summer break, with no one around, to get the feel of them. Once fall came around, I bought a good fur felt fedora (actually, 2 modern Stetson fedoras). And now I'm wearing an Akubra Federation IV that I'm really enjoying. I only got one "Indy" at work, but from a friend who knew I'd know she was teasing. A few odd looks, but not many. And yesterday, standing around having a conversation with a couple of colleagues while wearing my Fed IV, the college president walked into view nearby...for the first time wearing his own black fedora. There were several double-takes from him to me--looks that said, "Am I missing something?" I haven't caught him yet to compliment him or find out what type of fedora he was wearing.
In any case, wearing the lid will feel a little odd at first, but as you feel more and more comfortable with it, it will quickly become second nature. I feel naked going outside without a wide brim on my head now. And while the Stetsons were a convenient way to start, knowing what I know now, I definitely would have begun with Akubra's Fed IV or Stylemaster if I could do it all over again.
Have fun--after all, it's only a hat!