"But if the schnoozle gets wet, isn't there a chance of transmitting the moisture to the pad. Oh, are we talking about using the schnoozle with a downpad, right?"
Since the water is not going to go through the bag, just ensure you're storing your stuff inside the bag, the part that would also hold the air, so that doesn't get wet. The nozzle part is protected by snapping it into its mate when you're not using it.
"Also worried about a puncture which would prevent inflating the pad. Would that mean taking 2 schnoozles?"
As Stephen already said, just put some tape on the puncture and you're good to go, but I'd think the chance of a puncture is pretty low unless you're not paying attention when you pack.