Kote means "wrist", for sure. But even if you hold the hand, it is the wrist that is twisted - actually, even more so.
Actually "tekubi" 手首 (literally "arm neck") means wrist.
"Kote" 小手 is more usually translated as "forearm".
In kendo, the gauntlets are also called "kote" and they cover the entire hand and up to the middle of the forearm.