Make dressing: Force chutney through a sieve into a bowl and whisk in lime juice, oil, cayenne, and salt to taste. Dressing may be made 1 day ahead and chilled, covered. Bring dressing to room temperature before using.
Make marinade: In a large non-stick skillet dry-roast paprika, cumin, and coriander seeds over moderate heat, stirring occasionally, until fragrant and several shades darker, about 2 minutes, being careful not to burn them, and transfer to a bowl. Cool spices and stir in remaining marinade ingredients and salt and pepper to taste.
Pat shrimp dry and add to marinade, stirring to coat well. Marinate shrimp at room temperature 15 minutes. Alternatively, shrimp may be marinated, covered and chilled, up to 1 day. In a large non-stick skillet heat oil over moderately high heat until hot but not smoking and saute shrimp in batches, turning once, until golden and cooked through, 3 to 4 minutes.
Transfer shrimp with tongs to paper towels to drain and cool slightly. In a large bowl gently toss together shrimp, watercress, coriander sprigs, bell peppers mangoes and dressing.