I still have several of these in my gun cleaning box and they work well for good cleaning. Not sure if the Hoppes are the same but looks like midway discontinued them.
I ended using a variation of Ed’s Red and it’s all clean and sitting back in the safe now. It takes a lot longer to clean a revolver but it sure does give time to appreciate the things.
You have the right idea, IMHO. Twenty-two revolvers (and all other varieties of .22 handguns) don't need their bores brushed, just the charging holes in the cylinder. Using a .25 caliber bore brush on the cylinder holes works pretty well. I use Hoppe's Elite products. I clean and dry under the extractor star (double action). I use a lot of wooden toothpicks to get at the nooks and crannies. For guns I regularly take to the range, I only clean after about 500-600 rounds. For those I depend upon for defense, I clean after every range session. For those I'm not going to shoot for a while, I try to clean them completely before putting them away. I dislike cleaning guns, although the new striker fired pistols have spoiled me with their ease of disassembly and cleaning. Now, I absolutely hate cleaning revolvers and 1911's.