Preheat a grill to medium and brush the grates with vegetable oil. Whisk 2 cups water, the sugar and 2 tablespoons Old Bay in a large bowl until the sugar dissolves. Add the shrimp and set aside 10 minutes to marinate.
Remove the shrimp from the marinade and pat dry with paper towels. Toss the shrimp with the olive oil in a large bowl and season with 1 teaspoon Old Bay. Thread the shrimp, okra, wax beans and scallions onto eight 10-inch skewers; set aside.
Combine the melted butter, sherry, Worcestershire sauce, lemon juice and the remaining 1 teaspoon Old Bay in a small bowl. Grill the kebabs until marked and the shrimp are just cooked through, 2 to 3 minutes per side. Remove from the grill and brush with some of the sherry butter. Serve with lemon wedges and the remaining sherry butter.