Your gray water system consists of the following basic components, ranked lowest to highest:
1. Gray water tank dump valve and pipes
2. Gray water tank
3. Shower pan and plumbing
4. Kitchen sink and plumbing
5. Gray water tank vent (comes out on the roof)
Your bathroom sink probably drains into the black water tank. If it does drain into the gray water tank, it would rank between 2 and 3 on the list.
So, the shower pan is the true indicator of when then gray water tank is full and when stationary, the shower can hold approximately 10 gallons before overflowing onto the floor.
But your concern is the slosh, going to the dump station.
If the water is visible in the shower drain but not yet flowing into the shower pan, a tight fitting plug, as others have suggested, should be fine.
If the water is flowing into the shower, you will want to remove as much as possible before going to the dump station. A towel placed at the bottom of the pan along with a drain plug should neutralize any slosh of water you can’t bail out of the shower pan
To be absolutely sure, you can drain off some of the gray water into a bucket (the larger the better) using the gray water dump valve. Definitely a two person job as it is hard to position a bucket under the drain valve. Hopefully you have a hose you use to flush with that is not used for fresh water. You will also need to replace the dump valve cap
with one that has a provision for connecting a garden hose. Hook the garden hose to the dump cap and position one person with the bucket downhill from the trailer. The other person is going to work the dump valve and will open and close the valve based on instructions from the person at the bucket. Important, make sure you know which valve is associated with the gray water and the black water (they are usually marked Waste and Sewer). Double check with your trailer user manual if in doubt.
You can take the bucket to the nearest restroom or dump station to empty out. Or, if your black tank has capacity, dump it down your toilet. Five gallons drained from a gray tank that has not yet overflowed into the shower should provide more than enough margin of safety from sloshing.
Disclaimer, common sense prevails here, I am not responsible for spillage or any other accidental issue which may arise following my suggestions.