avataraang17, I have actually had the opposite concern in the past - I'm whiter than a bedsheet, but my dream costume is Tia Dalma from POTC.
I've decided that I'll just go for it, and if anyone comments about my race...well, I can't change that, so tough cookies.
But as others have said, your race doesn't matter when it comes to costuming. Heck, most anime characters are Asian, and many of us here are totally not. ^_^ Make a great costume and go have fun in it. That's really all that matters.