The K-Hornet is the Kilborne version(most common) of the Improved Hornet case, the AI is the Ackley version. You will have to do some research try googling each and compare dimensions. That said there are many versions of each depending on who's ordering the reamer. The nice thing is it headspaces on the rim so you should be able to fire standard 17 Hornet factory loads in it and measure the fired brass. Check with C&H for dies or order a custom die from FL Hornady(quite reasonable) and their standard 17 Hornet seater should work fine.
Arguably the best place to research this may be over on the Saubier forum http://www.saubier.com/forum.html. Expect you will be quite pleased shooting 20 gr projectiles. Id skip the 25 gr v-max options in this rifle though, as odd are you are working with a 10 twist barrel. 10 twist was more common though you can verify with a tight patch and a cleaning rod.
It might be smarter to just set the barrel back and have it rechambered to Hornady Hornet, then you'd KNOW for sure what you have, and if needed, just buy the factory ammo (and it shoots very, very well in my CZ 527).
You can roll a turd in peanuts, dip it in chocolate, and it still ain't no damn Baby Ruth.
In the TC 17 K-H, I'm using the Ackley brass and RCBS 17 K-H dies.
The 17 H-H is shorter so would make a very short-necked case when fired in the A-H or K-H.
Bruce
I was thinking of going this route. 17 Ackley Hornet brass fire formed and then reloaded with K Hornet does. I’m assuming I have to have those custom made.
“One thorn of experience is worth a whole wilderness of warning.” - James Russell Lowell
It might be smarter to just set the barrel back and have it rechambered to Hornady Hornet, then you'd KNOW for sure what you have, and if needed, just buy the factory ammo (and it shoots very, very well in my CZ 527).
The factory 20 grain VMAX shoots very well in my #1 rebarreled to 17 Hornady Hornet.