Cut off base of celery, and separate into stalks. Wash under cold water, using a stiff brush. Cut 6 inner stalks into 2-inch pieces (reserve remaining outer stalks for other uses). Set celery pieces aside.
Combine cream cheese, mayonnaise, Worcestershire sauce, salt, pepper, and 1/8 teaspoon paprika in a small mixing bowl; beat until well blended. Stuff celery pieces with cream cheese mixture. Chill. Sprinkle with additional paprika.