You can own almost any knife you please save for a select few like switchblades and "ballistic knives" (these those weird Soviet things that shoot their blades off).
Carrying around is another matter. The names "Hunting/ Survival/ Tactical" are irrelevant. It's a matter of the size and function. In NYC (but not the state), it is illegal to carry any knife at all openly and you have to keep them concealed. Yes, this is backwards from most places where a "concealed weapon" is a crime.
Knives with one-edged blades under 4 inches are fine. NY State has a weird badly written law on "Gravity knives" where if a cop can "flick" a knife open with one hand and it also locks open, it is illegal. The courts have allowed cops to hold the blade and shake it real hard so that it opens, and sided with the cop on the matter. So if you carry it should be a slip-joint knife or one that has a really tight screw so it will not flip by inertia.
There is generally an exception for knives used for hunting/fish or a specific job (like a seafood chef), but you have to be going to or from that place where you do that activity. You cannot just carry because you want to. Knives that have the visual appearance implying they are for fighting or other offensive use are illegal to carry in the state, as they are built for the purpose of being weapons.
It is generally illegal to carry any knife for self-defense. What that means to you is when a cop asks you why you have it, do not say that's your reason.
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