I have flown in and out of all 4 NY area airports (JFK, LaGuardia, Newark & White Plains) a total of 8 times with firearms, 5 different airlines, never had a problem. Just the normal declarations and inspections. Same for returning. I will say the inspections have varied from "please let's see the gun" to "please let's see the ammo". No one has ever checked to see if a gun is loaded, I doubt they'd know how.
It has nothing to do with NY laws, NY doesn't govern airline security. It's the FAA and the airlines.