Whisk together mayonnaise, milk, vinegar and pepper in a medium bowl. Add blue cheese and stir to mix.
Prepare grill or preheat broiler. When grill is hot, add wings and cook over medium flame, covered, until cooked through, 20 to 25 minutes, turning occasionally with tongs. Transfer wings to a large bowl, drizzle hot sauce over wings and turn with a rubber spatula to coat.
Peel and chop carrots, quarter and slice tomatoes, thinly slice celery, and quarter and slice cucumber. Put vegetables in a large salad bowl, add lettuce and toss well.
Arrange wings on plates. Serve with salad and blue cheese dressing.