La Guardia and Kennedy are fine if receiving through DElta. Technically you can't even have them shipped to Newark...that is a violation of NJ F&W laws, though I am sure they do it.
To give you an example, I have an authorization letter from NJFW allowing me transport venomous reptiles to Newark for shipment only(no other possesion aside from to/from airport is authorized). I usually ship NW Air Cargo (because Delta cares not 1 ounce about their customers). Because NW had closed I once tried to ship hots to Little Rock using DELTA DASH (NW Air Cargo didn't serve Little Rock) with someone elses account who was a verified shipper. The Delta attendent said because the actual verified shipper(to whom the snakes were going) was not authorized by NJFW, they would not allow the shipment.
There are some other glitches..e.g, you can ship NW CARGO without being a verified shipper(and they are very helpful too)....BUT NW Closed their terminal at LGA and only accept incoming shipments at JFK...hence the reason why I applied for the Authorization to ship from Newark. This is yet another reason why it would be so much easier to live in another state.