From the ATF website, but as stated don't know if NY has added to this:
Q: May a nonlicensee ship a firearm through the U.S. Postal Service?
A nonlicensee may not transfer a firearm to a non-licensed resident of another State. A nonlicensee may mail a shotgun or rifle to a resident of his or her own State or to a licensee in any State. The Postal Service recommends that long guns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms. Handguns are not mailable. A common or contract carrier must be used to ship a handgun.
[18 U.S.C. 1715, 922(a)(3), 922(a)(5) and 922 (a)(2)(A)]
Q: May a nonlicensee ship a firearm by common or contract carrier?
A nonlicensee may ship a firearm by a common or contract carrier to a resident of his or her own State or to a licensee in any State. A common or contract carrier must be used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm.
[18 U.S.C. 922(a)(2)(A), 922(a) (3), 922(a)(5) and 922(e), 27 CFR 478.31 and 478.30]
Q: May a nonlicensee ship firearms interstate for his or her use in hunting or other lawful activity?
Yes. A person may ship a firearm to himself or herself in care of another person in the State where he or she intends to hunt or engage in any other lawful activity. The package should be addressed to the owner. Persons other than the owner should not open the package and take possession of the firearm.
"Regardless of whether justified of not, you will feel sad about killing another human being. It is better to be sad than to be room temperature." - Joe B Fricks.
01 FFL, GOFFA, NRA, GOA, IAVA, VFW, ABATE of Iowa D15.