I think the problem with a 12-gauge pistol, even if it had a rifled bore, is that anything over 50 caliber is considered a Destructive Device. DDs are NFA, and still need paper.
There are a couple of things to think about with a SxS pistol.
First is "hammered or hammerless". Hammerless guns cock on the opening. Thus, the longer the barrel, the more leverage, and the easier it is to cock. And, the SHORTER the barrel, the less leverage, and the more difficult it is to cock. Denny's Guns, ten years or so back, brought in a bunch of Italian 20 gauge guns that had never had a buttstock attached, so he could make pistols and sell them a AOWs. In the article I read he mentioned how they had to rework the action, so it could be cocked with the ten-inch barrel. With a hammered gun, it opens easily, no matter how short or long it is, as the opening of the gun has nothing to do with the cocking of the hammers.
Then you have stock-shape. Anyone that has ever fired a Mossberg Cruiser, or similar, with a pistol grip at 90 degrees to the stock, is aware that they are painful, in an 8-pound gun. They are MORE THAN painful in a 4-pound gun. When fired they recoil UP, twisting your wrist. The stock on a Remington Witness Protection gun, on the other hand, has the gun recoiling BACKWARDS, pushing your shoulders. Much less painful.
Third is accuracy. Shooting a shotgun or rifle from the hip is not too difficult, as the shoulder stock is held against the hip, allowing you to use your body to help aim. When there IS no shoulder stock, you (or anyway, I) have a tendency to shoot left, as shown in this diagram.
http://s17.photobucket.com/user/therealalpo/media/Guns/hipshootingdiagram.jpg.html
Attempting any type of aimed fire is quite difficult without a shoulder stock. The two best ways are to pull backward on the grip with the shooting hand while pulling forward on the forearm with the non-shooting hand. This locks the gun in place, and allows fair accuracy, although it is a tiring position to use. It does not feel "normal", like just pulling the gun back into your shoulder does. The second way is one-handed, like a pistol. This is not too back, although (with MY gun) the back of the trigger guard tends to bang the hell out of the middle finger.
I have fired mine with two different types of ammo. Challenger (Canadian) target loads, 1 1/8 ounce of birdshot, both 7 1/2 and 9, and S&B (Czech) 00 Buckshot, 9-pellet. The target loads had much more recoil. The only explanation I can come up with for that is that the target loads were made with a fast-burning powder, and completely burned in the eleven inches of barrel, imparting all their recoil, while the buckshot was loaded with a slower powder, did not completely burn, therefore kicked less.
http://s17.photobucket.com/user/therealalpo/media/Guns/Cowboy/Mississippi10.jpg.html