Prepare salmon: In a small bowl, mix salt, sugar, dill, fennel, and pepper for the cure. Line a rimmed baking sheet with a very long piece of plastic wrap, letting it hang over ends. Sprinkle with 3/4 cup of cure. Set salmon, skin side down, on top. Cover fish with remaining cure. Wrap in plastic and chill about 4 hours.
Rinse fish; pat dry. Dry baking sheet, set a cooling rack in it, and set fish on top. Chill uncovered until tacky, 1 to 3 hours.
Meanwhile, make dressing: Whisk ingredients in a bowl and chill until used.
Make salad: With a mandoline or vegetable peeler, cut half of squash into thin ribbons and put in a medium bowl; set aside. Halve remaining squash lengthwise. In a large bowl, toss it with olive oil and 1/2 tsp. each salt and pepper.
Let salmon stand at room temperature. Light a full chimney of hardwood charcoal or a gas grill and heat to medium (about 350°). If using a gas grill, soak applewood chips in a bowl with water at least 30 minutes; set aside. Grill seasoned squash (set aside bowl with oil), turning, until barely softened, 10 to 15 minutes. Return to oil in bowl, let cool, then cut into chunks and toss to coat.
Meanwhile, cut 2 pieces of foil a bit bigger than salmon and crimp edges together. Cut holes in foil with a knife tip 2 in. apart and widen each to the size of a dime. Brush salmon all over with canola oil and set on foil. To cook over charcoal, let fire cool to low (250° to 300°). To cook over gas, reduce heat to low (250° to 300°). Drain wood chips and place in a smoker box. Or wrap in 2 layers of foil, poke 12 half-in. holes with a knife, and set pouch on a burner. Cover grill and wait until chips smoke, 10 to 15 minutes.
Grill salmon skin down (for any kind of grill), covered, until fish is just firm to touch but still rare in center, 15 to 25 minutes. With 2 wide spatulas, ease fish off skin onto a cutting board; save skin on foil. Tent fish loosely with clean foil and let rest at least 15 minutes. Meanwhile, if skin isn't crisp, return it on foil to grill and cook a few minutes longer. Set aside.
Add onion and shaved squash to grilled squash. Drizzle salad with half of dressing, add remaining 1/2 tsp. each salt and pepper, and toss to coat. Arrange salad on 2 large platters. Cut salmon into 12 portions and set on top. Garnish with large pieces of crisp salmon skin and dill sprigs. Pass dressing at the table.
Make ahead: Through step 4 up to 3 hours, or the rinsed, cured fish up to 1 day.