Big change of pace: once you cut into a cucumber, the fridge becomes your best friend. Cut cucumber goes in the fridge, no question. Wrap the cut end tightly in plastic wrap or store it in a sealed container.
It’s like that moment when you open a bag of chips—you can’t put the whole bag back on the counter. Once exposed, you need to protect it. Same with your cuke.
But here’s a pro tip: cut off a thin slice from the cut end before eating it the next day. That slice tends to get a little weepy, but the rest underneath will still be perfectly crisp.