Ok if you're really serious about this:
One of the supply houses-Midway or Brownells-make a brass rod. One end goes into a hand drill and the other accepts cleaning attachments depending on your bore size. Place the rod in the drill, soak the attachment with solvent, insert into chamber, hit the drill trigger and run it up and down the bore. To speed things up attach a nylon cleaning brush on the end. Five or six passes up and down and you will have it clean as it needs to be.
One warning: Hold onto the barrels tightly or they will be torqued out of your hand.
Or you can hold them in a padded vise and not worry.
Overkill, but if it makes one happy.
Dad rigged one up similar, made from scratch, used 0000 steel wool on the end and whatever was handy for a 'cleaner'. Rem-Oil, WD-40 (oh the humanity right?), CLP, and a half dozen others that are out there. Bore looked like a mirror after two passes and all our shotguns broke clays and killed birds with no issues.
You're right about holding tightly. If the barrel gets away from you, the ring on an 870 that goes around that magazine will beat your knuckles to pieces.