First, I always peel standard-issue, dark green cucumbers. They're often waxed, and I don't want to eat the wax, plus the skin has a tendency to be bitter. I usually seed those cucumbers as well, because the seeds are big and surrounded by watery (soggy) flesh. Second, I neither peel nor seed English cucumbers, commonly called hothouse cucumbers, because the skin is thin, generally unwaxed, and seeds are small. Last, cucumbers get weepy, so rather than make a watery mess of things I think of them as a last-minute ingredient. If I make a cucumber salad a little ahead, I drain off any water that accumulates before adding the dressing at the last possible minute.
I use cucumber for crunch in my tuna salad. Some orange segments, chopped onion and walnuts, plus a little salt and pepper round out my recipe. I use tuna packed in olive oil, so there's no mayo in my tuna salad -- but you could add dollop. I tend to eat my tuna as a sort of dip on potato chips, but as a sandwich or on top of half an avocado it's a pretty good option.