black powder residue is easy to clean. i use plain warm water. hot water can cause flash rusting when it evaporates. i have even used cold water our of a creek to get the worst of the fouling, then hit it with some warm water when i get home just to make sure its clean.
i have tried warm water with downy, it worked very well BUT i found it would negatively affect the finish on the wood of the stock very quickly so i stopped, you probably wouldn't have that issue on a double barrel.
i have used warm water and windex but didnt notice any real difference over plain water.
i have also bought a name brand black powder cleaner.pure snake oil. yes it works but its a waste of money.
there are probably as many ways to clean black powder guns as there are people to tell you, but its not hard to clean. they didnt have windex 200 years ago and they got by just fine. its harder to clean milsurps after shooting corrosive ammo than it is to clean your black powder guns so get out there and make some smoke, just for the love god clean them when you are done.