1. Make glaze: In a small saucepan, combine 1/4 cup lime juice, rum, sugar, and ginger; bring to a boil over high heat. Reduce heat; simmer, whisking occasionally, until slightly thickened, about 3 minutes. In a small bowl, whisk together cornstarch and 1 tablespoon water; stir into lime-juice mixture. Cook, stirring, until thickened, about 30 seconds. Remove from heat; let cool.

2. Thread shrimp onto 8 skewers, using 4 shrimp per skewer. Season on both sides with salt and pepper. Thread mango slivers onto 4 skewers, using 2 pieces per skewer. Brush shrimp and mango all over with glaze.

3. Heat grill to medium-high; oil grates. Place shrimp and mango skewers on grill; cook, turning once, until blackened in spots and shrimp are opaque throughout, 3 to 4 minutes.

4. In a large bowl, whisk together remaining tablespoon lime juice with the oil; season with salt and pepper. Add watercress; toss to coat.

5. To serve, divide watercress among four plates; top each with 2 shrimp skewers and 1 mango skewer.