From The Seat of Our Pants, at the Public. Photo: Joan Marcus Three years ago, my predecessor in this job, Helen Shaw, pointed out that The Skin of Our Teeth is “the show you do when the world is ending.” Bang on. In that sense, it’s hardly surprising that — including The Seat of Our Pants , Ethan Lipton’s new musical adaptation of Thornton Wilder’s rangy, genre-mashing behemoth, now getting its premiere at the Public — New York has seen three Skin s in less than a decade. The play’s immortal,