In places where the laws are that stringent on firearms they're also probably ultra stringent on crossbows and pellet guns. I haven't been able to find the penal code for crossbows in NYC but the crossbow websites all indicate they're not allowed. So, buying a crossbow instead of a rifle is not a viable option.

However, you probably aren't going to be hunting in the city proper, so why not buy and store a gun somewhere else? You could buy a rifle in upstate New York, rent a storage locker and store the gun there. Nothing illegal about it. You may or may not be able to reach it in a major disaster, but you certainly can't reach a gun you don't own in an emergency. And, you can take it with you camping and hiking where its allowed.