Your rifle becomes a short rifle if you shorten the barrel shorter than 16" or if when you remove the stock the overall becomes less than 26". So depending upon the length of your receiver your lower barrel length might be 18 or 20" long if the receiver was short enough that with a 16" barrel and stock removed it does not make 26". Federal law allows the measure to be with the folding stock open, some states require the 26" to be stock folded so a longer barrel is needed.
Your pistol becomes a short rifle, if a stock up put on it and you don't also add a barrel extension to take it up to the 16" and 26" overall requirement.
So you could put the buttstock on your pistol and weld a silencer onto the barrel long enough to make the length ok and not have to register the pistol as a short rifle.
Having an extra stock that will fit the pistol is going to be a tough road to convince the legal system that you had no intent to create an illegal weapon with it.
On to the topic did you know that your fake silencer is not a real silencer and must be returned to the importer for replacement for a fake silencer.