I use a regular old 22 caliber bore tech rod and VFG pellets.
The difference between 22 rimfire and 22 centerfire is .002-.003 inches.
Use a one piece coated rod along with a bore guide and all will be well.
Bore snakes are ok in a pinch, but once the snake gets dirty with unburned powder and other junk, you can be rubbing all that abrasive along your crown.