I have a .22 Outdoorsman (1937) that I wouldn't dream of dry firing without snap caps. I won't take credit for discovering this, but here's the absolute best solution for .22 snap caps I've found.

They're hollow wall anchors for #4-#6 screws. A box of 100 is about $3 or so at Home Depot. If your forget what size you need, just remember yellow. That's the color code for this size from all manufacturers.

These anchors fit the cylinder and cylinder recesses in the K22 exactly. In fact, I can load them into a Ruger Mark III magazine and they feed and eject just like live ammo.

Buy a box and share them with your .22-owning friends. I wouldn't be without them.