Ooh...very good plot twist.

Archenemies forced to combine their magic to face something which threatens them both...but no wands, very odd indeed.

Ol' Dumbly-dore could do wandless magic and surely Voldy can too, but Harry...I don't know. He's could learn but not even the other Hogwarts professors showed they could use magic this way. If we had seen even the simplest of magic without a wand from someone else I would believe that Harry could do it, too, but the total lack of examples throughout the series makes me doubt it.

This conclusion poses another question...if it's not wandless magic they're doing, what is it?