Actually the compression won't change. The load of the water COULD show the compression lower if the starter is having trouble turning over the engine, but the compression done on the trailer will be what it is.
I have had a problem like this before, but need more info. Try this, can you start the ski up still strapped to the trailer, back it in to the water while it is still running and see if it will continue running or if it will die.
It is sounding to me like the battery might not have enough juice to make the ski start in the water. This happened to me on a GSX with a weak Walmart battery, in the water it didn't put out enough power to get the ski to spark. Out of the water it would fire up with less of a load.
Another ski I had where it would fire up out of the water, but not in the water, but I could start it up on trailer and back it into water and it would die unless giving it lots of throttle. It ended up being a bent rotary valve that wouldn't allow it to idle. It needs to be perfectly flat and in spec with the rotary valve cover.
