I said a #26 because that's what is on both of my KT19s. and they run pretty well.... your observations may vary. IDK if it was in a Kohler manual or where, but I have read it somewhere that this was the OEM size carb for the Kohler carb used on the KTs, and the Walbro would have been a (different numbering system) #52.
though I have seen #30s come equipped on a M12 12hp single before....my Woods ZTR came to me so equipped, ran great with it
though when I mounted a #30 onto a 301 once it would backfire upon shutoff... (though the original K341 that this carb came from, didn't do so-- I "borrowed" the carb while I waited for Heli coils to arrive to fix the stripped threads that held the backing plate for the air filter on)
I'd look for a good used original Kohler carb and go thru it... though as I remember the throttle shaft and choke shaft were different from those used on #26 carbs,for the single cylinder engines. you can buy reproduction carbs from that "Isavetractors" guy but they are available many places/ as cheap as they are, I'm afraid the "you get what you pay for" kicks in.