I think you first need to see how sweet the watermelon is by itself. I poor quality watermelon will need more sugar a good one less. I think one of the recipes on Jack Keller's website called for about 2Lbs sugar (four cups). He also discusses this operation in great length which I have paraphrased below. I think what you need to do is measure the specific gravity of the watermelon juice by itself. If it is around 1.09 you should be ok.
Watermelon is kind of tricky. The juice can spoil before you can get the yeast started. Extract the juice, put in a crushed campden table, and refrigerate it for 24 hours. In that time make a yeast starter of some fast acting yeast (Montrachet).
When the juice is ready my big question is how do you warm it up so you can pitch your yeast without killing it? I would probably gently warm it up (or some of it) on the stove, then pitch your yeast.
The cold will not kill your yeast but make them a little sluggish. As the watermelon juice comes up to temp they will take off. A few wine yeast will ferment at 50 degree much. Some beer yeast do there best work at that temp.
All 5 kids plus one 14 year old friend in beach condo in daytona. I need a vacation from the vacation. But it was nice to spend a week with my oldest who is old enough to be on her own. But I did have a good time.