Would you recommend using a brush? Or would that damage the barrel? I have a cleaning kit that includes a brush that looks like copper, maybe. I don't use it very often.
Not all metals are created equally. In fact not all types of the same metal, steel for instance, are created equally. The copper brush won't hurt it.
Case in point. When I was young and stupid I got a barrel bushing for a 1911 wedged in there during removal. Tried wacking as hard as could be with a rubber mallet and no go. Didn't have a brass hammer. All I had was a regular claw hammer. I sighed and told myself, "well I guess I will just replace the bushing." I gave it a few good wacks and it came off. Afterwards I looked at the barrel bushing for damage and couldn't find any. The hammer, however, had a noticeable dent in its face. The tool steel wasn't as strong as the steel in the bushing.