Thanks everyone!
Let me elaborate. These would just be 1-2 night trips and the holding tank is right beneath the sink, inside the camper. I'd take it out when I get home and empty it. I do trail races that are sometimes far enough away to require staying overnight. It would be for use at the races. It would mostly be used at night.
I don't mind putting the p-trap in if it's useful. Just didn't want to if it isn't. I'm just not sure if I'll have enough room to use a pipe like I linked to in addition to plumbing in a trap. I probably only have 18" (maybe?) between the bottom of the sink and the grey water container.
