Have you tried to call them to see if they will build you a 1300KT with a .22 LW barrel? If it's available for other CCS guns, then I can't see why the wouldn't be able to.
I'd recommend considering some other gun entirely if you are wanting it for hunting.Reason being: slow fps in .22. Some 460 fps?My 1377 only wounds even the smallest birds. So, I don't shoot at critters with it. (unless I'm wanting to, ahem, wet them off like that coon that was raiding the hawk's nest in my back yard,)
Have a 1322 carbine, 14” bbl, shortened valve-spring.Otherwise, valve is stock. 12 pumps throws .22 Hobbies @ 560, with just the slightest puff of air retained.Kills big fox squirrels stone-dead. I prefer .22, for the usual reasons😊