It's very interesting, but I'm afraid your theory of cross-pollinating isn't the answer. Even if they did cross, i.e. bees carried pollen from squash to cucumber, or the other way around, the vines wouldn't immediately make fruit that was the result of the cross. The seeds inside your cucumbers or squash would be the combination of the two. So you'd have to let a fruit (either squash or cucumber) mature all the way to brown and dry, so the seeds were mature and then plant those seeds to get the result of the cross-pollination.
I think probably incomplete pollination is the problem. Those light green cukes look like the Armenian type. Do you know what type you bought? Or did you start them from seed, and still have the seed packet.
Anyway, to get complete pollination, try brushing some pollen from a mature male flower (with pollen visible and no fruit behind it) to a female flower (has a baby fruit on the stem behind it) using a little artist's paint brush. Be sure you pollinate cukes to cukes, and squash to squash. It's easy to tell the flowers apart because the squash flowers will be a lot bigger.
