Pro Shot makes excellent one-piece stainless steel cleaning rods. With regard for use with a .22LR, they are available in .22 and .20 cal. diameters. I have one for use at the range and another for use at home. They are available at site sponsor Nordic Marksman
https://www.nordicmarksman.com/Rods.html
I prefer the .20 cal rod because it reduces the risk of unwanted contact with the inside of the bore.
https://www.nordicmarksman.com/36-Rifle-20-Cal-w-20-Cal-Jag.html This adapter allows it to use all standard accessories
https://www.nordicmarksman.com/17-Cal-Adaptor-540-thread-to-832-Thread.html
Always use a bore guide designed for your rifle. They, too, are available for many different rifles at Nordic
https://www.nordicmarksman.com/Bore-Guides-2.html
Always use appropriate-sized patches. If they are too big and too tight, it will increase the risk of the rod bending and contacting the bore. Be aware that not all jags marked .22 are the same diameter -- some are a little wider than others.
I used a Tipton carbon fiber .22 rod for years, but it eventually broke at the base of the handle. The Pro Shot rod is very well made and should last a long time.