To prepare sauce, combine cucumber, yogurt, dill, and garlic in a small bowl.
To prepare salmon cakes, remove bones and skin from salmon. Place chickpeas in a medium bowl; partially mash chickpeas with a fork. Stir in salmon, breadcrumbs, and olives. Combine parsley and next 5 ingredients (parsley through egg whites) in a small bowl; stir into salmon mixture. Divide mixture into 12 equal portions, shaping each into a 3/4-inch-thick patty.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 6 patties; cook 4 minutes. Carefully turn patties over, and cook 4 minutes or until golden. Repeat procedure with 1 1/2 teaspoons oil and remaining patties. Serve with sauce.