I think Legilimency requires a wand (or at the very least, extreme skills to do it wandlessly) because there's actually an incantation to perform it. Where Occlumency was just closing off your mind from the invasion and we're never told Harry has to do anything other than focus on not letting Snape in to his mind.

So yeah, I'd say Occlumency doesn't use a wand at all, where Legilimency would.