Hello,
I apologize for my bad English language.
I'm sure that K doesn't stay for Crudo (= Raw, i.e. not heat treated to remove brittleness), but I don't know what is its real meaning. Perhaps it COULD stay for Chromium, but I'm not sure about this at all!
I don't know, too, in which year the Cogne KM0 (0 = Zero) steel was presented; I can tell only that you can find it in the fifth edition of the manual L'impiego e il trattamento dell'acciaio published by Cogne in October 1959.
Supercromato isn't a variety of KM0 steel: it means that the barrels made with it were internally chromed in a high quality way.

Best regards,
Maxm