How short can a shotgun pistol be? And do y'all know of any company that sells them? If I'm not mistaken a handgun that shoots shotgun shells can be as short as you want it (like the judge). I just can't find anyone that manufactures them. Mossberg makes a 14" pump action but it's 26" long. I was looking for something a little shorter. Maybe brake action 10" or something similar.
The Judge is a .45 Long Colt revolver with a rifled bore meaning it is not a shotgun. It is incidental that the chambers are slightly elongated and .410 shotgun shells can be chambered.
Smoothbore and shorter than 26" overall is an NFA item classified as an AOW (Any Other Weapon) unless it happens to have a shoulder stock...in which case it would be defined as a short-barrelled shotgun if the barrel is shorter than 18".
Editing to add:
I haven't yet found a break-action shotgun that comes from the factory with only a grip and not a full shoulder stock. The significance is minor as modifying a stock to a grip and cutting the barrels shorter would require the same NFA process as taking a pistol-grip break-action shotgun and cutting the barrels.
If you wish to go through the NFA process ($200, prints, waiting), then you can basically have any length of shotgun you are comfortable using.