If I get called she once or twice a year, I won't care. Even if there was a risk of outing me, most people aren't thinking like that. They'd think, "Haha. They called you a she, Danny, and you've been living next to them for 16 years." It would be funny or strange, but they probably would right off assume, "OMG ->-bleeped-<-." Most people don't think about transsexuals unless they're on the news like Thomas Beatie.
But yeah. I'd play it off the way you did. They don't need to know it's you right away. If you grow closer, then maybe you can tell them. But they're practically strangers to you.