It depends on where the wrist-watch actually is. If the wrist watch is actually strapped around your wrist, then you are "wearing" the wrist-watch. If, however, the wrist-watch is in your hand, in a pocket, or in a bag, for example, then you would be "carrying" the wrist-watch. "Carrying" implies the act of transporting or moving something, whereas "wearing" implies something has been affixed (or attached) to your person.

I guess the 2d. But I'm not sure.