If'n you're worried about the barrel turning whilst you tighten the barrel nut, a couple thick (1/4" or so) swatches of leather like from an old belt, to wrap the barrel about 3-4" from the nut, lock a pair of vice grip - the kind with the roundish jaw - on the leather clad barrel, pucker up good & tight and lock them shut.

As you push on the barrel nut wrench you can push the vice grips in the opposite direction so it doesn't move.
I've yet to mar or damage a barrel using the vice grip & leather method and since we all know barrel swapping never happens once, you'll have your "special tool" for the next swap job.