I've Park'ed a few rifles and most recently an H&R 929 pistol. In the rifles I used rubber plugs to complete satisfaction; none of them budged. I used corks in the H&R and they too worked fine.
Honestly, I wouldn't even bother plugging a shotgun barrel. With the slick surface present on the interior of a shotgun barrel, I doubt much of the solution will adhere to the metal and even if it does, it should be easy to clean it out.
Years ago before I started doing my own Parkerizing, I sent a rifle I had built off to a 'smith for a Parkerizing job. When it returned, the interior of the barrel had Parkerizing in it. I just cleaned the barrel and have been shooting the rifle ever since. Evidently it had no effect on the barrel because it's one of the most accurate rifles I own!
35W