What other action would you use to use a wand?
I still think a new action type Use Magic Item will be needed, I can see the casting thing for most but for things like potions as far as the rules go that falls clearly under Use Item to me.
To be honest, I don't see that quaffing a potion with Cunning Action is an issue. But using it to cast 'Ice Storm' should be right out.
But trying to cheese weasel an attack out of it is more like the player trying to use Cunning Action on the DM.