Soak 8 bamboo skewers in warm water for 30 minutes; drain. Insert 2 bamboo skewers through 2 shrimp so the skewers form an X; repeat with the remaining shrimp. Rub the skewered shrimp with 1 teaspoon of the oil.
In a medium bowl, combine the sliced fennel, pistachios, lemon juice, lemon zest and 2 1/2 tablespoons of the olive oil. In a small dry skillet, toast the fennel seeds over moderately high heat, stirring, until fragrant, about 3 minutes. Add the seeds to the fennel salad and season with salt, pepper and the sugar.
Heat the remaining 1/2 teaspoon of olive oil in the small skillet. Add the shallot and cook over moderately high heat, stirring, until softened. Remove from the heat and stir in the tomato and watermelon. Transfer to a small bowl and stir in the chopped basil.
Heat a grill pan. Season the shrimp with salt and pepper and grill over high heat until opaque throughout, about 2 minutes per side. Spoon the fennel salad onto 4 plates. Set the shrimp skewers on the fennel, top with a spoonful of the salsa and serve at once.
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