Keeping the solution out of the barrel doesn't take anything special. Put an empty case with a spent primer in the chamber and tap a cast bullet into the muzzle(just enough to keep it there).
The 'acid' isn't terribly harsh. It's phosphoric acid(the active ingredient in Naval Jelly for rust removal) that just degreases the steel. Fairly tame stuff as acids go, but don't get it in your eyes or on your hide.
Had my .243 Lube-Rited(black phosphate. Same idea with different chemicals) long ago. Didn't have a cast bullet of the right size. The inside of the barrel got done. Didn't make any difference at all.
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