Whisk together the shallot, mint, dill, lemon zest, olive oil, and lemon juice in a small bowl. Add the sugar, salt, and the white pepper.
Cut the cucumbers in half crosswise. Using a vegetable peeler, peel long strips to form ribbons, and place the ribbons in a salad bowl. Add the dressing to the cucumber ribbons and toss to combine.
Arrange the cucumber ribbons on four salad plates. If using, tuck slices of salmon in among the ribbons, or drape them loosely over all. Serve immediately.