Cucumbers and melons (or gourds/pumpkins/squash) are a totally different species, so no, they can't cross outside of a laboratory with people who can splice genes. (This HAS been done in labs between cukes and melons by the way, but highly unlikely in a garden)

Cucumbers of different varieties can cross though, or a bird or animal may have carried some gourd or squash seed to your garden, or some cucumber that found it's way into your compost was an odd variety or was the product of some cross from two different cucumbers that you bought or got from a friend.

Those crosses don't show up until the year after the fruit sets, the fruit itself looks perfectly normal.

Squash, gourds and pumpkins are all in the squash species, and so can interbreed and produce seeds so the next generation can be a cross between a yellow crookneck and a pattypan and such.  At least the crosses are usually within the summer or winter types due to the blossoms being ready to fertilize at the same times… usually.  (yeah, I know)  They are not related closely enough with cucumbers or melons to cross naturally with them though.

Some people think that a crop of melons that just don't taste good must have crossed with something odd, but usually it's from crummy weather, or soil problems.  Cukes are very sensitive to water issues too.

I wouldn't be afraid to taste something like that that showed up in my garden, things they may have crossed with are just not likely to be a problem.