I used clear plastic drop cloth for half my Crimson Sweet and Marketmore 76 cucumbers (on raised beds) and the difference in growth is far more dramatic than I was expecting. Those with the plastic mulch are easily twice the size on average with a few closer to triple the size. However, they also have a soaker hose underneath the mulch and under the soil (by only an inch or so), so maybe the watering method is helping as well.
The only drawback to using clear mulch that I've run into is the grass attempting to grow underneath.
I was going to go the black plastic route, but I heard it can become so hot as to actually damage the leaves that touch it. Watermelon seems to be a creeping-type plant, so that worried me.
Anyway, I think you'll be happy using mulch. It conserves water, too!