Season skate with salt and pepper, then dredge both sides in flour. In a large saute pan, heat 3 tablespoons oil over high heat until just smoking. Add half of the skate, and cook 4 to 5 minutes. Turn skate, add 1 shallot and 2 tablespoons wine, and cook until skate is golden brown and cooked through, 4 to 5 minutes more. Remove and keep warm; set aside. Repeat with remaining skate.
Meanwhile, in a medium saucepan, combine cockles, wine, and remaining shallot. Cover, bring to a boil, and cook until the cockles begin to open, 3 to 4 minutes. Add shrimp and saffron citronette. Cook, covered, until shrimp are opaque. Season with salt and pepper. Stir in parsley.
Heat remaining tablespoon oil over medium heat in the same saute pan that the skate was cooked in. Add arugula, and cook until just wilted. Season with salt and pepper. Divide arugula among four warmed bowls, and top each with a skate wing. Divide shellfish and broth evenly among bowls. Sprinkle with parsley, and serve immediately.