In a pot of boiling water, blanch the snow peas for 45 seconds to 1 minute. Transfer with a slotted spoon to an ice bath to refresh, then drain well on paper towels. Set aside.
In a small bowl, to make the dressing, whisk together the scallions, 1 tablespoon of the cilantro, the mint, rice wine vinegar, lime juice, ginger, garlic, sugar, pepper flakes and salt, and whisk to combine and dissolve the sugar. Add the oil in a steady stream, whisking to combine. Adjust the seasoning to taste.
In a large bowl, combine the lettuce, watercress, red bell pepper, and cooked snow peas. Toss with about 1/4 cup of the dressing to lightly coat.
Divide the tossed salad among 4 plates. Arrange the shrimp in the middle of the greens and the papaya along the outer edges of the plates. Drizzle lightly with the remaining dressing. Sprinkle with the remaining 1 tablespoon chopped cilantro, and garnish with the nuts, cilantro sprigs and chives. Serve.