I find the easiest solution, is to force yourself, mentally, not to give a (insert swear word here) about what other people think. I don't know how well you pass, it shouldn't matter anyway, people stare regardless. I stare, you stare, we all stare. I just noticed that being f2m I always assume people are "reading me", when reality people just stare. I pass 24/7 365 days a year, always get the "sirs" Mr's", but when I see someone "staring" I always jump to the conclusion they must read me.
Like someone else said, go in with confidence. Keep in mind, these people you're seeing at the stores, customers, cashiers, etc, you more than likely will NEVER see again, so who cares what they're thinking.
Once you figure out your size, if you're still having anxiety about going out and shopping, ebay has good stuff, at great prices.