OMG, thank you! I must never leave the house without a copy of OotP again.

I didn't realise Snape told Harry so explicitly to use his wand. That clears that up! My guess would be that Harry, as a beginner, needs the wand to learn the skill. Or Snape doesn't want to admit that Harry's a pretty powerful wizard!

I also think Snape must have mastered wandless Occlumency to be able to fool Voldemort and I suspect (with no real evidence) that he could perform Legilimency wandlessly too. I think there are several places where it's hinted at in the books (by Dumbledore and Voldemort as well as Snape).