Ok, so let me start by saying that I'm not a lawyer and I make no claims that I know what I'm talking about, I'm an average dumbass. The RSA's are all linked in the threads tacked at the top of the forum.
When it comes to NH RSA's and questions like this it's important to read "definitions" that are often in the start of each chapter as they set the guidelines for each RSA (and questions about them).
That I can find (important disclaimer) under RSA 159:1 definitions of pistol/revolver is "159:1 Definition. – Pistol or revolver, as used herein, means any firearm with barrel less than 16 inches in length."
NH fun and games RSA 207:7 covers having a loaded rifle or shotgun in a loaded vehicle but if you look at the definitions in that chapter rifle and shotgun aren't defined, they only define a "firearm" which would include handguns and even starter pistols (specifically mentioned in the definitions).
So IMO since rifles and shotguns aren't defined by statue (that I'm able to quickly find), the much more clear definition given by RSA 159:1 would apply. If you go by this definition any short barreled rifle or short barreled shotgun would be considered by law a handgun.
If anyone has any other information to add please do. I've been thinking about getting a shockwave (you hear that Cookiemonster?) and I've thought about the legalities for carrying/transporting it as well.