Only law NH has on knives (unless you're a felon or a minor) is
156:16 Carrying or Selling Weapons:
The named knives appear to all be terms that historically refer to fixed double-edged blades. None of these terms appear to have any relation to non-auto folders, and no length limit is proscribed. In case law, I only found one instance of a single edged "hunting knife," but the defendant was a convicted felon (which is a separate law) who was getting in a fist fight downtown and tried to pull the knife on responding officers. Even then, they had a hard time convicting him.
The northern New England states seem to be rather weapon/blade friendly in my experience, even the LEOs. Heck in Vermont, you don't even need a permit it stick a pistol in your pocket.