Hi - It looks like your Japanese cucumber plant is showing symptoms of a leaf spot disease, which is not uncommon for cucumber plants. You can prune out and discard those leaves in the trash (not compost). Harvest the cucumbers regularly as soon as they ripen; this will help to keep up the plant's productivity. Keep up with your watering now that the fruits are developing. The spacing by the zucchini is not a problem. It is fairly typical for cucumber plants to decline gradually in the growing season; try to get as much as you can by frequent harvesting. 
https://extension.umd.edu/hgic/topics/cucumbers

Christa