I've used my outdoor shower.. in the woods, in remote locations.
I've also used the indoor shower without sewer hookup, since I dry camp most of the time.
Is your gray tank small enough that you are concerned about filling it up at the race?
When I dry camp, I always follow the "GI Shower" technique.
Turn water on, get wet. Turn water off, lather up with soap, turn water on, rinse.
In and out. Saves water, and doesn't fill up the tank like a shower would if you left the water running the entire duration.