Combine celery, radishes and cucumber in large bowl. Peel hard-cooked eggs. Separate egg whites from yolks; chop whites. Stir whites into vegetable mixture in bowl until evenly distributed.
Mash hard-cooked yolks in small bowl until smooth. Whisk in oil, salt, pepper, sugar and jarred salad dressing until smooth. Continue to whisk, adding lemon juice and vinegar until well blended. Toss with chopped salad.