In a small bowl, combine the mayonnaise, capers, lemon juice, 1/2 teaspoon mustard and 1/4 teaspoon pepper. Cover and refrigerate until serving.
In a small skillet, saute the onion and celery in 1 teaspoon oil until crisp-tender. In a bowl, combine the onion mixture, salmon, 1/2 cup bread crumbs, egg and remaining mustard and pepper. Shape into four patties; coat with remaining bread crumbs. Cover and refrigerate for 10 minutes.
In a large skillet over medium heat, cook salmon patties in remaining oil for 5 minutes on each side or until lightly browned. Serve with caper mayonnaise.