I would be inclined to leave the cover off, since the cucumbers need to be pollinated in order to develop. If you think deer or other animals might be an issue, you could use some chicken wire or something similar to keep the animals out but let the bees and other pollinators in. If you think slugs might be the issue, I'd use something like "Sluggo," or you could try some beer traps for them. If the leaves aren't being badly chewed up, just showing some holes here and there, I wouldn't worry too much. Interestingly, this year is the first time I've ever seen earwigs in my garden and there seem to be a lot of them... but I also have a "bee house" for leafcutter bees so I'm used to seeing quite a few holes in all the leaves!
Best of luck to you - it seems like everything is a juggling act when it comes to encouraging the beneficial bugs and protecting plants from the bad ones.
Also, for future reference, there are cucumbers that don't require pollination, which could be grown under protective covers without a problem. I'm growing one this year called 'Green Light' and this article lists some other varieties (although I'm not sure if any of them are "space saving" types - mine grow on a trellis):
https://www.bountifulgardener....