For the remoulade: Stir together the mayonnaise, capers, hot sauce, lemon juice, Worcestershire sauce and scallions in a small bowl; refrigerate until ready to serve.
For the shrimp: Toss the shrimp with the flour, paprika, and 1/2 teaspoon salt in a large bowl. Whisk the buttermilk and egg together in a medium bowl. Mix the French fried onions and panko in a shallow bowl. Working one at a time, shake the excess flour off the shrimp, and then dip to coat in the buttermilk. Let the excess buttermilk drip off, and then coat thoroughly in the onion-panko mixture. Place on a parchment-lined baking sheet and repeat with the remaining shrimp.
Fill a large deep skillet with about 1/2 inch of oil and heat over medium-high heat until it registers 375 degrees F on a deep-fry thermometer. Add half of the shrimp and fry, turning once, until golden brown on both sides and just cooked through, about 3 minutes. Transfer to a paper-towel-lined plate to drain. Return the oil to 375 degrees F and repeat with the remaining shrimp. Sprinkle with salt while hot out of the fryer.