Finely grate enough ginger to yield 1/2 teaspoon; set aside. Cut remaining ginger into 1/4-inch slices. Bring 5 cups water, sliced ginger, peppercorns, and 3 tablespoons lemon juice to a boil, covered. Reduce heat to low, and add shrimp. Cover, and poach until just cooked through, stirring occasionally, about 4 minutes (do not let liquid boil). Drain, discard ginger and peppercorns, and place shrimp in a bowl of ice water for 5 minutes. Drain shrimp; refrigerate at least 15 minutes and up to 1 day. Peel, devein, and cut shrimp in half horizontally.
Whisk together remaining 2 tablespoons lemon juice, the grated ginger, fish sauce, and oil in a large bowl. Add shrimp, melon, radishes, and half the scallions, and toss well. Add jicama, and gently toss. Divide between 2 plates, season generously with coarsely ground pepper, and garnish with remaining scallions.