Cook pasta according to package directions, drain. Immediately rinse with cold water, drain well. Meanwhile, whisk together the mayonnaise, vinegar, relish, white pepper and pepper sauce in a small bowl; set aside in the refrigerator to chill.
Combine the cooled pasta, ham, cheese, red pepper and scallions in a large bowl. Stir in the mayonnaise mixture just before serving. Garnish with paprika.