Roughly chop rosemary leaves and combine with garlic in a bowl. Add chicken; turn to coat. Drizzle with lime juice and sprinkle with salt and pepper. Chill, covered, 1 hour.
Peel fine strips of skin lengthwise from cucumber. Slice cucumbers thinly. Divide watercress into small sprigs.
To make mustard and lemon dressing, whisk sour cream, yoghurt, milk, mustard, oil and lemon juice in a large bowl until combined. Add salt and pepper to taste. Add cucumber, watercress and herbs to bowl. Stir to coat completely with dressing.
Heat oil in a nonstick frying pan over medium heat. Add chicken and cook, turning occasionally, 8 to 10 minutes, until cooked through. Remove from pan and set aside for a few minutes.
Arrange cucumber and watercress salad on individual plates. Cut chicken crosswise into thick slices; add to salad.