q tips mate!!!
I used like 10 q tips lubed with your oil of choice, shoved them down my rifle barrel and came out in the reciver. Just keep pushing them down the barrel one at a time, pushing on the other one, then use a stick to finish them out.
I have been using brass brushes in all my barrels, I notice nothing in the 3 years I been shooting. I recommend you just keep an eye out for it, bore light to check. What type of 22 rifle? if it's a cheap $150< rifle I wouldn't care much. But if it's a Ruger 10/22 or something better yes I would.
SHTF vs TEOTWAWKI you ask? SHTF, just some crap on the ceiling and walls, TEOTWAWKI end of the world as we know it. Orignally made by 9mm/®™©