I normally try to stay far away from law discussions in NY, but it seems no one else has responded so I will do the best I can. First important thing to note is that you're not in New York City. Not only do they have much stricter laws, but there enforcement of existing laws is highly aggressive, bordering on absurdity. Upstate is not really that bad and the cops tend to be a lot more reasonable.
The gravity knife thing comes from a specific interpretation of the state law (knife related matters are under Article 265 of the
Penal Code). NY Courts have ruled that any knife with a locking blade can be gravity knife, if you can open in centrifugally with one hand. This includes grasping the blade the flinging the handle downwards, which applies to nearly all locking folders in existence. However, enforcement of this specific interpretation is primarily in NYC, while other parts of the state tend to be more lenient.
The remark about no concealed carry law is a misinterpretation. The law (265.01) makes any carry of an illegal knife, openly or concealed, a crime. This is important to remember because many states allow open carry of certain knives while making concealed carry illegal, but NY doesn't work that way. If it's an illegal knife type, you can't carry it at all.
The matter of a hunting, fishing or trapping license is also something of a misinterpretation. 265.20 states that the restrictions under 265.01 shall not apply to:
That is, it only applies when you're actually going hunting, fishing or trapping. Mere possession of a license doesn't grant blanket permission to carry a switchblade or "gravity knife" in everyday carry.