Damage To Cucumber Fruit

You may have had a visit from a rodent or the slug/snails, or maybe an insect pest. We can’t say for certain from this photo what caused the damage, but as you mention you haves some of these organisms around, one of them is the likely cause. Rodents usually will take more tissue when eating, but slugs/snails may do more shallow damage. You can look for the slugs/snails at dusk and dawn and pick them and dispose of them, or you can look for them in moist, dark hiding places during the day (sometimes you’ll even find them hiding on the undersides of plant leaves) and dispose of them; sealing them up in a bag and putting them in the trash is an easy quick way. Here’ more info about cucumbers and their common pests:
http://www.ipm.ucdavis.edu/PMG/GARDEN/VEGES/cucumbers.html