Here is your picture. I think I would run a garden type hose from the sink to the washout port of the tank (small opening up near the handle with a cap). When ready to dump it, just unscrew the hose, put the cap on the port, take to dump station and hook a regular dump hose from the tank (large port) to the dump hole.
Grey water can and often does smell just as bad or worse than the black tank. I would not run it on the ground unless camped alone in a large remote area. Your neighbors will not like you one bit if you run it on the ground. It is illegal, as far as I know, to do that in any state campground and most private ones. If you leave the caps on until ready to dump there should be no smell problem in the camper.
Barney
