x2 on the boresnake, I spray a little CLP on the cleaning part run it through and I'm usually G2G right from that point, run it through again if I don't think I got it all. Both were in stock at my local Gander right next to each other on the shelf.
I see them different places, but it looks like the tip is not smaller than my .17 cleaning tip and that once loaded with a partial patch has a tough time getting down the bore of the 22.
I think more damage is done to .22 bores and crowns by cleaning them, than by leaving them alone. When I feel like I must clean one, I use a piece of plastic line trimmer. On one end of the line, I melt a ball. I cut the other end of the line at a sharp angle, so a cloth cleaning patch can be pierced and threaded onto the line. I use solvent and/ or Kroil on the initial patch, let it sit and then use clean dry patches. I never use a metal bore brush or snake on a good .22 bore. I only use a bronze brush (.25 caliber) to scrub out the chamber.
Pull the cleaning rod thru instead of trying to push it thru. Thought I was going to kink the cleaning rod the first time I cleaned the.17.. Run the cleaning rod down the barrel, attach brush, pull back out.
Before you try to feed it down the breech, hold the brass, pull it tight and hold it for a while. That will thin out the feeding portion of the snake and help it slip through the bore.
I have thin metal wire, I wrap cleaning cloth on the end around it and put Hoppes on it and pull through. My 17 is a bolt action and I just drop the bolt. After its set I pull a clean cloth through and repeat til clean. For my 22 I have a smaller patch head that my grandfather made (he was a tool maker) and its small and causes no issues.