Bring 5 cups water to boil in large saucepan over high heat.
Stir in 1½ pounds shrimp, peeled, deveined, and tails removed and 1 tablespoon table salt.
Cover and let stand off heat until shrimp are firm and opaque, about 6 minutes, shaking saucepan halfway through.
Fill large bowl halfway with ice and water.
Transfer shrimp to ice bath and let cool for 5 minutes.
Drain shrimp and pat dry with paper towels.
Cut half of shrimp into ½-inch pieces; coarsely chop remaining shrimp into pieces smaller than ½ inch.
Spread 2 tablespoons salted butter, softened, evenly on outer sides of 4 New England–style hot dog buns.
Toast outside of buns in 12-inch skillet over medium heat until deep golden brown, about 5 minutes.
Transfer buns to serving platter.
Whisk ¼ cup mayonnaise, 2 tablespoons minced celery, 2 teaspoons minced chives, ¼ teaspoon grated lemon zest, ¼ teaspoon salt, and pinch cayenne together in medium bowl.
Add shrimp and gently toss to combine.
Season with salt to taste.
Divide 4 leaves Boston lettuce among buns, if using.
Divide shrimp mixture among buns and serve with lemon wedges.
