In a large pot, bring salted water to a boil. Add the shrimp and cook for 2-3 minutes, or until they turn pink and opaque. Drain and transfer to an ice bath to stop the cooking process. Once cooled, chop the shrimp into bite-sized pieces.
In a medium bowl, combine the mayonnaise, lemon juice, dill, chives, Dijon mustard, Old Bay seasoning, salt, and pepper. Mix well to create the dressing.
Gently fold the chopped shrimp into the dressing until well coated. Cover and refrigerate for at least 30 minutes to allow the flavors to meld.
While the shrimp mixture chills, heat a skillet over medium heat. Add butter to the skillet and toast the hot dog buns until golden brown on both sides.
To assemble, place a lettuce leaf in each toasted bun and generously fill with the shrimp mixture. Serve immediately.