I have owned a K9 and rented a P9 a couple of times. You said you wanted a lightweight, the P9 as you know is substantially lighter.
I don't think recoil is much of an issue for the P9, I find it very comfortable to shoot with a nice trigger, so why not carry less weight.
The Ruger LC9 is based on the Kel-tec PF9, which I have owned, and which had substantial recoil and muzzle flip, enough so that I sold it.
Supposedly, from a test I've read (in Gun Tests), Ruger shaped the grip on the LC9 to have less felt recoil, but I would still think it would kick harder than the Kahr P9.
It does not sound like Ruger has trimmed felt recoil to Kahr levels, and from all of the accounts the trigger on the LC9 is not a good as a Kahr trigger.
So, given your choices, my first pick would be the Kahr P9 ( or actually, its much less expensive version, the CW9), my second pick the K9. There appear to be alot of happy LC9 owners out there, so you probably can't go wrong.