Pat shrimp dry and place in a large bowl. Add the celery and green onions; toss gently to combine.
In a separate bowl or large measuring cup, whisk together the mayonnaise, lemon juice, vinegar, dill, Old Bay and sugar. Add the mayonnaise mixture to the shrimp mixture; toss to coat. Taste and season with kosher salt and pepper. Cover and refrigerate until ready to serve.
Butter the cut sides of the hot dog buns. On a griddle or in a cast iron skillet, toast the buns buttered-side down, until golden brown. Fill each bun with shrimp salad. Garnish with additional dill or freshly-chopped parsley.
