It appears Kevin Kern replied at 12:58 today. In case it got hung up in your spam folder, here is his reponse:

Thank you for your question to "Ask Extension". I have provided the following information on why and how to prune watermelons. 

Pruning the vines without fruit can be done to control vine spread and potentially reduce the risk of plant disease. To increase fruit size the number of fruits per plant can direct more energy into developing fewer larger fruits. For large varieties, removing all but two or three well shaped fruits is suggested. For smaller varieties , keep four to six fruits per plant. To encourage additional fruit set remove misshapen or unhealthy fruits early on to redirect the plant's energy towards producing more and better quality fruit.

I hope that you find this information useful and as always Happy Gardening.