For a shotgun to count as a smoothbored pistol (AOW, with $5 transfer fee), it must be manufactured with a pistol grip. It can't have a shoulder stock on it at any time, or else it becomes a short-barreled rifle or shotgun. So if you just chop off a shotgun stock, or replace the stock with a pistol grip, it's still a shotgun. It has to have left the factory with a pistol grip on it.
Also, making a 12 ga "derringer" isn't as simple as making a .410 one. The .410 derringers do have rifled barrels and will take .45 LC ammo. A 12 ga "derringer," even if rifled, would be a "destructive device" rather than a handgun, and subject to a $200 manufacturing/transfer tax, because the bore diameter is greater than .50".