Preheat grill or broiler to high. In a large bowl combine shrimp, 1 tablespoon fish sauce, 1 tablespoon brown sugar and 1 tablespoon rice vinegar, and salt. Toss to mix and thread onto parallel skewers, pushing the shrimp together on the skewers. Set aside.
In another bowl, combine the vermicelli with the remaining fish sauce, brown sugar and vinegar, cucumbers, radishes and half the mint leaves. Toss to mix and place on a platter along with the lettuce leaves.