I know you say it isn't possible, but I have something in my garden that has to be a cucumber/squash hybrid. I have pictures. It tasted like a cucumber and looked like a cucumber on the inside, but was short and chubby and orange, w/ thick squash-like skin. I had planted cucumbers and several varieties of squash and we got squash hybrids galore, and these odd cucumber-like specimens. Any thoughts?
Cucumber/Squash Cross Pollination
Certified GKH Gardening Expert
Cucumbers and squash are in the curcubit family, but they cannot cross pollinate. It is like humans and monkeys. Same basic family, but not compatible. Here is an article from the Iowa Extension Service on why it can't happen: https://www.ipm.iastate.edu/ipm/hortnews/node/981
Now, there are cucumbers that look and taste as you describe. One that comes to mind is a Mexican Sour Cucumber. You may have a mislabled plant or seed in your garden that was mislabled by the company that sold it to you.
They could also be under pollinated cucumbers, meaning some of the seeds got pollinated while others did not, which can result in one side filling out, while the other side does not. This article explains more: