. . . a head covering can be anything that works: there's no particular intrinsic special power in a kippah.

You've overlooked the obvious solution: baseball cap. Just beware wearing a Yankees yarmulke in Brooklyn. Or a Mets one in Manhattan. Or a Red Sox one anywhere in the metro area. You're probably best off supporting a team no one cares about, like the Kansas City Royals or the Arizona Diamondbacks.