It's possible to clean a BP rifle such as yours with only the use of BP solvents. I'd use 3 out of 4 sections of a Hoppe's BP Cleaning rod with a .41 caliber Kleen-bore brass cleaning jag attached to it. Then I'd cut homemade rectangular cleaning patches out of old tee shirts (about 3.5 X 4 inches or so), moisten it with BP solvent, and fold it over a few times until it fits very tightly in the bore. Keep swabbing the bore while refolding the patch to maximize all of the different clean sides of the patch. Repeat with maybe a half dozen patches until the patches come out absolutely clean. Stubborn deposits can be brushed out with a Tynex or bronze bore brush, but only if necessary. Then remove and soak the nipple and clean out screw in alcohol or solvent and clean inside the drum and all around the lockwork very thoroughly with solvent too.
Unscrew the tang screw if necessary and remove the front half of the stock along with the barrel.
Clean out any powder residue that enters the back of the lock and under the barrel. Then lubricate everything appropriately with oil (on a cotton swab) in the lock, and bore butter or similiar inside the barrel.
The bore butter will help to loosen & lift out any remaining residue, and after a day or two go back and swab out the bore another time or two to insure that all the residue has been removed. Make sure you remove all of the residue from the nipple & drum & cleanout screw threads too. Then reapply some more bore butter in the barrel with a nore butter saturated cleaning patch, and apply some to all of the threading with a cotton swab. Don't forget to scrub the hammer face clean too, and anywhere else powder residue might accumulate on the brass around the crown. Then coat all of the brass by rubbing it with a silicon cloth.
This procedure requires a little more elbow grease than if using soap and water, but doing it thoroughly can be very effective at removing most all harmful residue. But the patches must be very tight and it must be repeated until everything is very clean and bright. It can be laborious, but preserving the rifle for the long term depends on doing it right.
A brass or plastic bore protector/guide will help to protect the muzzle and crown from being damaged by the repetitive up & down motion of the cleaning rod.
A patch worm will help to pluck a patch out of the breech if it drops off the cleaning jag during barrel cleaning.