In NYS women can carry anything up to a .45 handgun for semi-auto, and up to a .357 if it’s a revolver. You can get one from pretty much anywhere and just walk up to a cop and pull it out and show him that you can chamber a round, remove the mag and eject the round in the chamber. The officer would then sign you off as long as he’s near his cruiser they should have the required paperwork. You can do it in pretty much any town court or city hall or whatever too.
Men have to jump through more hoops though. Good luck!