Ok. Reading the statute, I would say there is no way the cousin could possess or fire the weapon. Below is cited where he is prohibited. All of the exceptions are listed in 265.20, but I found no exception in there that would allow the cousin from shooting a gun at a range.
§ 265.01 Criminal possession of a weapon in the fourth degree.
A person is guilty of criminal possession of a weapon in the fourth
degree when:
(1) He possesses any firearm, electronic dart gun, electronic stun
gun, gravity knife, switchblade knife, pilum ballistic knife, metal
knuckle knife, cane sword, billy, blackjack, bludgeon, metal knuckles,
chuka stick, sand bag, sandclub, wrist-brace type slingshot or
slungshot, shirken or "Kung Fu star"; or
(2) He possesses any dagger, dangerous knife, dirk, razor, stiletto,
imitation pistol, or any other dangerous or deadly instrument or weapon
with intent to use the same unlawfully against another; or
(3) He or she knowingly has in his or her possession a rifle, shotgun
or firearm in or upon a building or grounds, used for educational
purposes, of any school, college or university, except the forestry
lands, wherever located, owned and maintained by the State University of
New York college of environmental science and forestry, or upon a school
bus as defined in section one hundred forty-two of the vehicle and
traffic law, without the written authorization of such educational
institution; or
(4) He possesses a rifle or shotgun and has been convicted of a felony
or serious offense; or
(5) He possesses any dangerous or deadly weapon and is not a citizen
of the United States; or
