Peel English cucumbers. Halve lengthwise; scrape out any seeds with a teaspoon. Slice cucumbers very thinly on the diagonal.
Thinly slice radishes. In a large colander, toss vegetables with coarse salt. Top mixture with a plate that fits inside colander; weight with a heavy object. Drain in sink 20 minutes; squeeze vegetables in paper towels to dry.
Transfer to a bowl; toss with minced red onion, cider vinegar, olive oil, and 1 teaspoon sugar; season with salt and ground pepper. Serve immediately.