The PPSH barrel has a lip on it I think? You'd have to either lathe the barrel stub to handle the lip, or more easily just lathe it off.
The barrel probably doesn't have to be welded to the shim, you could probably rely on pressure alone if you made it a nice press-fit. The original barrel pin will probably be going through the PPSH barrel to keep it pinned in place.
It would be fairly easy to do I think.