Can Bone Skewer choose a unit from the opponent champion zone?

No, Bone Skewer cannot choose a unit from your opponent's Champion Zone.

According to RiftJudge FAQ #9526, while the Champion Zone functions as an extension of your hand, it is a distinct zone and does not count as being in your hand. Because Bone Skewer specifically instructs you to "choose a unit from [the opponent's] hand," a unit in the Champion Zone is not a legal target.