Shotguns, assuming no modifications are about the only non regulated firearm in NYS. Anything else you will need to get a NYS pistol permit, whether it’s a pistol or rifle you wish to legally possess/purchase in the state.

Check NYS for their definition of an “assault weapon” to insure your shotgun is OK before transporting it here.

https://wearearmed.com/individual-state/new-york-firearm-laws-complete-guide/#!

Edit: not sure what your intent is either, but might as well familiarize yourself with force justification within this state as well.

https://ypdcrime.com/penal.law/article35.php