Heat oven to 400°. Drain salmon and flake into a bowl; stir in breadcrumbs, 2 tablespoons mustard, mayonnaise, 1 tablespoon dill, 1 tablespoon shallot and capers until well combined.
Form into 8 patties (1/3 cup each); let rest 5 minutes. In a large, ovensafe pan over medium-high heat, heat 1 tablespoon oil; cook patties until golden brown, 4 minutes per side. Transfer to oven and bake until hot to the touch, 10 to 12 minutes. In a bowl, combine yogurt, 1 tbsp lemon juice and remaining 1 1/2 teaspoons mustard, 1/2 tablespoon dill and 1/2 teaspoon shallot; season with salt and black pepper.
Toss arugula with remaining 1 tablespoon oil and 1 tablespoon lemon juice, and salt and pepper. Serve salmon cakes with yogurt sauce, arugula salad and lemon wedges.