Make sauce: Combine yogurt, dill, oil, lemon juice, salt, and pepper in a bowl. Cover and chill until used.
Heat grill to medium-high (about 450°).
Make salad: Cut cucumbers lengthwise into paper-thin strips, preferably with a mandoline. Put in a bowl with herbs and shallot; chill until used. In another bowl, mix oil, lemon juice, salt, and pepper; set dressing aside.
Prepare salmon: Rub all over with oil and sprinkle all over with salt and pepper. Fold a 12- by 20-in. sheet of heavy-duty foil in half crosswise. With a knife tip, poke dime-size holes through foil about 2 in. apart. Oil one side of foil.
Set foil with oiled side up on cooking grate. Set fillets slightly separated, skin side down, on foil. Grill, covered, until fish is barely cooked through, 7 to 12 minutes. With a wide spatula, slide fish from skin to a platter and tent with foil. If you want crisp skin, continue to cook skin on foil until crisp, 2 to 3 more minutes. Remove foil from grill, then gently peel off skin, using your fingers or a wide spatula (skin may break into pieces).
Set crisp skin, if using, on plates and set the salmon on top. Discard any liquid from cucumber mixture in bowl, then quickly toss mixture with dressing and mound on fish. Garnish with fresh dill sprigs. Serve immediately with yogurt sauce (salmon skin will soften as it stands).
Note: Nutritional analysis is per serving.