Working with reproduction Brown Bess muskets at the museum where I worked, we developed a good way to clean the barrels after reenactments that did not require removal of the barrels. First we would remove the lock and clean that separately. A damp cloth would be used to clean the vent area on the side of the barrel and any powder residue on the stock or inside the lock mortice.
Next the vent would be plugged using a bamboo "fondue" skewer cut to about 4", taking care to see that it was water-tight. The gun would be set on its butt and using a funnel, a half-cup of Hydrogen peroxide would be poured down the barrel. A thumb would be placed over the muzzle and the gun inverted several times to get the solution to "work." (the barrel does get hot) After a few minutes, this would be dumped out and another half cup of peroxide would be added and the procedure repeated. After the second peroxide solution was dumped, pure water would follow using the same procedure.
Its not a bad idea to keep the lock side facing down, the gun on about a 45 degree angle, and have an absorbent cloth stuffed into the lock mortice while pouring liquids down the bore, just in case. I had used "Renaissance wax" on the underside of the barrels and in the barrel channels when the guns were new and unfired, so water did not easily get between barrel and stock.
After the pure water rinse, cotton muslin cloth patches would be used to dry the bore Once dry and clean, it would be lightly oiled using either "balistol" or Rig, or sometimes even automobile ATF as a rust preventative. After 15 years of service they are still in like-new condition.