I've never used a snake, and will probably get one some day, I use a Dewey for my .17's.
As far as scratching the bore with a rod, it is similar when cleaning a .22 because the rod is close to the bore diameter, the rod will touch the bore. Make sure that the rod is clean, wiping it off before use, between patches, and every few brush strokes. .22 target rifles have many thousands of rounds fired through them and are cleaned frequently with no damage when cleaned properly. A friend had to clean his Martini every 100 shots in a match or it would start opening up the groups. Stainless steel rods are less likely to be embedded with dirt particles than brass, aluminum or steel. Always clean from the chamber so you don't damage the muzzle or crown. Use a bore guide if possible, but I haven't found one yet for the HMR.