A little Hornet followed me home...

[jmoore]

I know of 22 Hornet inserts, but not K-Hornet. (Also 22 Rem Jet, of which I have six.)

Get also a .22rf bolt head and mod a spare firing pin, or just do a spare bolt for the rf.

Probably the best way to get a chamber insert for the "K" is to have one made, even an old .22rf barrel stub MIGHT do, but the front bit's going to be mighty thin! (Best to remove the insert rifling, I should think, if you go the salvage route. I think I'd start w/ a bit higher grade steel than the soft commercial rf barrel stuff.)
A regular Hornet insert MAY work, but it'll be plenty unsupported.

Slip fit they are, unless something's amiss (generally).