I use a bore guide on my match M1's and M1a's. That is the only way to clean these barrels. You take your time, be careful, and not rub the crown, the muzzle will outlast the throat.
What about rimfire barrels, are they more delicate than that of a centerfire barrels and is it ok to use a brass brush when cleaning. I don't clean my rimfire rifle barrels very often roughly every 2500 rounds or so for my 1022 and 3 or 4 hundred for my 9317 with the Otis kit using just patches, but I'm kinda nervous about using a brush.
Anschutz originally provided guidance about never, or hardly ever, cleaning their .22LR barrels. The last booklet I saw, they recommended very infrequent cleanings and never pushing a bristle brush through the muzzle. It was OK to push the brush out from the breech, but Anschutz wanted the brush removed and not pulled through the muzzle.
I asked a number of senior small bore shooters about cleaning a match 22 LR barrel. Opinions are all over the place. Some shooters never clean their .22LR barrels. Like 250,000 rounds and never cleaning. Others clean often. Because I started out as a highpower shooter who always does a detail clean after 88 rounds, I can't get out of the habit: I clean my Anschutz match barrel after each small bore prone match. I am pulling the bristle brush back through the muzzle. I guess I have 3000 rounds through the tube, my scores are improving, so heck if I know if cleaning hurts. I do use a breech bore guide. I use copper pistol brushes, nylon brushes, and always use bore solvent.
One gentlemen who was into benchrest rimfire, he cleaned at the end of each and every shooting session. He claimed that is what the winners did.
For a 10/22 I suspect you will have to clean the chamber or the wax build up will cause malfunctions. A friend had a Marlin Glenfield, must have shot bricks of ammunition through it never cleaning, but it started malfunctioning. It needed a clean.
Rimfire ammunition is totally covered with wax. The bullet is covered in wax/grease and so is the case. I believe the case is waxed to provide lubrication in these rimfire blowback actions. Under the pressures and heat of combustion the wax melts and lubricates the case, keeping the brass from sticking in the chamber, and facilitating extraction. Once that case is pulled from the chamber all that vaporized wax condenses in the action and eventually, you have to clean it out.
I have met shooters at the range whose blowback rimfires were so dirty their cases were not extracting. I took a magazine worth of their ammo, dropped oil on the cases, rolled the cases around in my hand, loaded the magazine. In each instance the shooter shot that magazine, and every oiled rimfire magazine after that without a malfunction. Oil will dissolve to a certain extent the wax build up in the chamber. Still, the guns needed to be cleaned.