The correct terminal type, per Dickey terminfo, is "kitty". (The PuTTY variant KiTTY is apparently also "putty".) And the terminfo database lends itself both to copying individual records and to having extra records in one's home directory.
Thanks for the insight :) I have always had a bit of 'why do I gotta know that' thing going on with terminfo, console and friends - this is making me want to dig a bit deeper!