I've no practical experience with .22 Conversion kits, but I came across information for one that was interesting.
I found a cartridge, tiny little, smaller than a .22 BB Cap. I finally identified it as a 4mm Uebungesmution round. (Smallest cartridge, biggest name.)
It was a German training round for a conversion kit for the Luger, and later P-38 pistols. It was strictly a single shot proposition. The illustration I saw show it in a P-08 Luger. The sub-caliber barrel apparently had a screw on (I'm guessing) chamber that fit in the 9mm chamber of the Luger. The barrel apparently threaded into this, then had a lock nut at the muzzle which also had a built-in front sight. Empties were poked out with a thin steel rod.