Place eggs in a medium saucepan and cover with cold water. Bring water to a boil and immediately remove from heat. Cover and let eggs stand in hot water for 10 to 12 minutes. Remove from hot water, cool and peel.
Slice eggs in half lengthwise. Remove yolks. Set aside whites.
In a medium bowl, mash egg yolks with a fork. Mix together with mayonnaise, shrimp, green onions, fresh dill weed, lime juice, prepared Dijon-style mustard, hot pepper sauce and ground black pepper.
Spoon approximately 1 tablespoon egg yolk mixture into each egg white. Garnish with fresh dill weed. Chill in the refrigerator until serving.