You'll want to get the fouling reduced to the point where it doesn't alter cylinder dimensions or cycling. Scrubbing guns to the point of sterilization is usually more harmful than leaving a little staining alone. Build up is one thing, cosmetics is another all together. That said, I've had a little luck with a good coat of Ballistol around the cylinder front, the strap, and outside the forcing cone before shooting. Most of the crud seems to wipe off. However, I haven't tried to shoot 300 rounds before cleaning either.
The black powder guys like it. It is mainly mineral oil with detergents. It cleans up with soapy water, and doesn't smell bad.
It's cheap also, you might like it.
If your cylinder is stainless, the lead cloths are excellent, per everybody else.