It all depends...
Do you have a " hot transit" where your baggage is checked through to destination? If so then it won't be a problem.If you have to take possession of the weapon/s and check them in again at another carriers desk then you will legally be required as a " non resident alien " to be in possession of a valid New York state hunting licence.
As bizarre as this sounds it is the only legal way you can be in possession of a firearm unless you have applied to the NSA for import permission for sports shooting,competition or trade purposes.
Apply for your NY hunting permit online.
