Only 15 minutes to a tasty shrimp sandwich? We can roll with that.
Whisk together mayonnaise, celery, lemon juice, hot sauce, Old Bay, salt, and pepper in a medium bowl. Stir together shrimp and half of mayonnaise mixture. (Reserve remaining mayonnaise mixture for another use, such as a dipping sauce or sandwich spread. Mixture will keep in an airtight container in refrigerator up to 1 week.) Cover shrimp mixture, and chill until ready to serve, up to 2 hours.
Trim just enough of the long sides of each bun to form two straight edges. Brush melted butter on the trimmed edges of each bun. Heat a large skillet over medium, and cook each buttered side until golden, about 30 seconds per side.
Divide shrimp mixture among buns, and slice each in half crosswise. Top with chopped celery leaves.