1Place eggs in single layer in 2-quart saucepan; add enough cold water so it is at least 1 inch above eggs. Heat to boiling; remove from heat. Cover and let stand 18 minutes. Drain; rinse with cold water. Let stand in ice water 10 minutes.
2Peel eggs; cut lengthwise in half. Slip out yolks; place in medium bowl. Mash yolks with fork until smooth. Reserve 1 teaspoon green part of onions for garnish. Stir mayonnaise, vinegar, salt, pepper sauce and remaining green onions into mashed yolks. Fold in shrimp.
3Fill egg whites with yolk mixture, heaping it lightly. Just before serving, top with cocktail sauce and reserved green onions.