Make the vinaigrette: whisk together 2 tablespoons grated horseradish, 1 1/2 tablespoons lime juice, 1 tablespoon fish sauce, 1/2 tablespoon light brown sugar and 1 tablespoon olive oil; season with salt and pepper to taste.
Prepare fried shallots: heat about 1/4 inch vegetable oil in a large skillet over medium heat until shimmering. Dust the shallot rings with cornstarch in a colander, shaking off excess.
Add coated shallots to the hot oil in an even layer and fry, stirring occasionally, until browned and crisp, about 3–4 minutes. Transfer with a slotted spoon to paper towels and season lightly with salt.
Preheat the oven to 400°F (200°C). Pat the salmon fillets dry and season both sides with salt and pepper.
Heat 1 tablespoon vegetable oil in a large oven-safe nonstick skillet over high heat until shimmering. Add the salmon, skin side down, and sear until the skin is browned and crisp, about 3 minutes.
Flip the fillets and transfer the skillet to the preheated oven; cook about 3 minutes more, or until the salmon is just cooked through.
Assemble: divide the cantaloupe among four shallow bowls and drizzle each with buttermilk; season lightly with salt.
Place a salmon fillet on each bowl of cantaloupe, spoon the vinaigrette over the fish, then sprinkle with lime zest and additional grated horseradish to taste.
Garnish each serving with celery leaves and the fried shallots, then serve immediately.