According to the BATFE Manual the separation of a Judge & like handguns verses a legal shotgun (minimum 18 inch barrel / minimum 26 inches overall) is that one is designed to be fired from the hand and the other is designed to fired from the shoulder. However, a recent BATFE ruling has classified a pistol grip shotgun as a friearm designed to be fired from the hand, but has not classified it as a "handgun". I know........this is a claer as mud, but this is typical of most any Federal Agency.
With that said..............IF you were to attach a stock of some sorts that would enable a Judge, or like handgun with a barrel length less than 16 inches, to be fired from the shoulder, then............it would be considered a short barreled rifle/shotgun and would require a Federal Tax Stamp (&200.00 I believe) and associated local & Federal paperwork. A rifle barrel must be a minimum of 16 inches long and have an overall length of 28 inches (if I remember correctly).
I can quote chapter & verse but I am short on time now. Below are a couple pictures of one of my defense shotguns. Mossberg 500 Cruiser/Persuader. Eight shot / 20 inch barrel.
FR&G
FR&G