Stainless Steel
My personal preference is to remove the stains from the front of the cylinder. They don't hurt anything because they are just stains. But I still preference removing them. To do that, use a treated lead removing cloth. Rub hard until the stains are gone. Birchwood Casey sells a good lead removing cloth as well as other manufacturers. The last time I used Midway's brand, it was worthless. That's all you need.
This is likely to draw comments, but another way is to spray break cleaner with no chlorine through the bore, through the cylinder chambers, & at the very front of the cylinder where the stains are. You must take care to keep the break cleaner clear of any non-metal surfaces, such as rubber handles. (Don't use break cleaner on any blued surfaces.)
Then, use regular solvent, bronze bore brushes, & patches to clean the weapon. Apply bronze hand brushes rubbing until the stains on the cylinder disappear.