1. Cook potatoes in large pot of boiling water until just tender. Drain. Transfer potatoes to large bowl and cool.
2. Mince egg whites. Add whites, radishes, pickles, celery and onion to potatoes. Mash yolks in medium bowl. Add dry mustard, prepared mustard and pickle juice. Add mayonnaise and milk and blend until smooth.
3. Pour dressing over potatoes and toss gently. Season with salt and pepper.