Internal surfaces of the chambers and bore can be cleaned using a fresh bronze bore brush, dry (no solvent or lube). Then use a cleaning patch saturated with solvent, allow it to sit and work for 10 minutes or so, followed by clean patches until nothing shows up on the patch.

External surfaces (cylinder face, inside frame around barrel breech) use a bronze brush, dry, scrubbing firmly. Then brush with solvent, allow it to sit and work for 10 minutes or so, and wipe clean.

Stubborn leading (forcing cone, chambers, bore, cylinder face): I like an old worn bore brush wrapped with strands of 0000-grade steel wool, run through dry to cut through the leading, then clean as usual. 0000-grade steel wool will not damage the bluing or the bore at all. That is what we used in the US Army to clean heavily fouled small arms from 5.56mm to 20mm, back in the late 1960's to early 1970's. I keep a hunk of 0000 in my cleaning supplies all the time and regularly find a use for it.

Purchased my 6" Model 19 in 1976, did several seasons of PPC shooting with .38 Special lead bullet loads, and this is how I have maintained the old piece. Still as tight and accurate as it can possibly be, and the finish is excellent.

I still buy new bronze bore brushes by the dozen, use them until they start showing significant signs of wear, then start using a new one. I always have a few well worn brushes to use with the 0000 for especially stubborn cleaning chores.