Preheat broiler with oven rack 6 inches from heat. Place salmon, skin side down, on a foil-lined baking sheet. Broil 5 minutes. Set aside until cool enough to handle.
Place panko, egg, shallot, capers, parsley, garlic, dill, lemon juice, smoked paprika, red pepper, 2 tablespoons mayonnaise, and 1/4 teaspoon salt in a large bowl. Mix to combine.
Remove and discard salmon skin; place salmon in a bowl, and mash with a fork. Add to panko mixture. Using your hands, mix until well combined. Shape mixture into 4 (3/4-inch-thick) patties (5 ounces each). Place patties on a parchment paper-lined baking sheet. Cover and chill 30 minutes.
In a small bowl, combine yogurt, Sriracha, vinegar, remaining 2 tablespoons mayonnaise, and remaining 1/8 teaspoon salt. Set aside.
Heat oil in a large nonstick skillet over medium-high. Place salmon patties in skillet; reduce heat to medium, and cook 4 to 5 minutes per side or until browned.
Spread aioli evenly on cut sides of toasted buns. Top each bottom bun with 1 salmon patty. Top patties evenly with onion slices and arugula; cover with top halves of buns.