Combine first 5 ingredients in a small bowl; cover and chill.
Place salmon in a food processor; pulse until coarsely chopped. Add breadcrumbs and next 6 ingredients (through 1/4 teaspoon black pepper); pulse 4 times or until well blended.
Divide salmon mixture into 4 equal portions, shaping each into a 3/4-inch-thick patty.
Heat a grill pan over medium-high heat. Coat pan with cooking spray. Add patties to pan; cook 2 minutes.
Carefully turn patties over; cook 2 minutes or until done.
Spread about 1 tablespoon mayonnaise mixture over bottom half of each hamburger bun. Top each serving with 1 salmon patty, 3 cucumber slices, 1 lettuce leaf, and top half of bun.
Spinach salad: Combine 2 tablespoons hoisin sauce, 1 tablespoon rice vinegar, 2 teaspoons canola oil, 2 teaspoons water, and 1/4 teaspoon chile paste in a large bowl; stir well with a whisk. Add half of 1 (5-ounce) package baby spinach, 1/2 cup yellow bell pepper strips, and 1/4 cup thinly sliced red onion to bowl; toss to coat.