Which tool to use as watercolor paper press
The answer is to pre-stretch the paper before painting, and leave it stretched until dry. 

To pre-stretch, wet the paper evenly, then tack down the corners to a drawing board with some slight tension. 

Using water activated tape (paper tape) tape the edges of the paper to the board with 1/4" to 3/8"s overlap on the paper smoothing out the tension as you go. You may need to reposition the pins as the paper flattens to the board. Regular art tape or masking tape will not work since the water undoes the adhesive.  

Once it is taped down let it all dry, and be sure to let the work dry after its done before removing it from the board. It should remain flat.

The only problem I have found with this is getting the paper tape off the edges of the water color paper. Sometimes it snaps off nicely, more often it remains behind so I just cut it off the board at the papers edge. If someone has a solution for this that gets the tape off and leaves a nice clean edge I would love to hear it.