Toss cucumber with its salt and leave in a colander for 15 minutes, then blot thoroughly with paper towels.
Meanwhile, boil cavatappi in water with the tablespoon salt until fully tender. Drain, rinse under cool water and drain thoroughly.
Mix yogurt, mayonnaise, lemon juice, zest, garlic powder, pepper, mint and red onion. Fold through pasta with the dry cucumber slices.
Cover and refrigerate for at least 30 minutes; the listed prep time includes this chilling.
Toss gently before serving cold and refrigerate leftovers within 2 hours.