A few years back I got a bonus seed pack from an online seed company. The seeds were of an Italian heirloom novelty variety called Barese Cucumber. If you harvest when young they can be used as a traditional cucumber. Let them grow to use as a melon. They have a downy peach like fuzz that can be wiped off. They are sweet and bitter free. When cut open the seeds are clumped around the center and are easily removed. If you seek something different it's a good choice.
I am wondering how the cucumber melons turned out. @Ed Wilson ? Do you have any pictures , and are you growing them again this year ? Here is one of the pictures that I found online; is this what yours looked like ?
Yes, those are the ones. Like everything else in my life, I downsized my garden so there would be no room for them, but now that it's been brought up, I may give them a try next year.