Short answer : Don't sweat it.
I've worn braces (not the transparent ones, the metallic ones) on both upper and lower teeth from 11 to 15 (in school) and then again from 21 to 24 (at work), during which time I had to undergo serious jawbone surgery which kept me away from work for a month.
I've been teased a lot by classmates when I was young (you know how cruel kids can be), even bullied sometimes, but the second time around, my coworkers were more than understanding and sympathetic. As people get older, they understand you don't wear braces to make yourself interesting or just for the sake of it, but that you have a genuine teeth issue. You might be seen as "the dude with braces" for a few weeks, especially if you're new at this job, but that will fade away pretty quickly.
The only thing you're gonna have to worry about is how braces may affect you physically. It's a long and painful road of teeth-hurting, inner-lip-scratching and gum-bleeding, and it will without doubt leave you with a severe hatred for dentists. But in the end, when you finally take them off, my God, what a relief it is ! And I've never been happier now that my crooked teeth are fixed, I learned to smile and if I had to do it all over again, I would.