I'd hang it over the side, vape it and put it back out of harm's way. You could always buy a cheapo ecig kit with the same connection and use it. Chances are, all you'd damage is the atomizer from soapy water ingestion, but why take a chance on a high end ecig when you can use something less valuable? The little ecig can be your backup anyway. We all need backups.
Truth is, a tube mod can be washed out in clean water and dried. We pour alcohol in Provari's from time to time to wash the circuit board. It's recommended in Provape's FAQ, but that's only something done when a Provari gets juice in the electronics for some reason. The atomizer connection is sealed pretty well.