Heat broiler; place whole pepper on a foil-lined sheet 6 inches below heat. Broil 10 to 14 minutes, turning until blistered all over.
Cover in a bowl 10 minutes; peel, seed, and blot dry. Finely dice; cool completely on a plate about 10 minutes.
Mix mayonnaise, yogurt, onion powder, cayenne, and pepper. Fold in cheddar and cooled pepper, keeping cheese visibly shredded.
Cover; refrigerate 30 minutes until firm and cold. Cooling and chilling are included in prep time.
Spread one-quarter mixture on each of 4 rye slices; close and cut diagonally. Serve cold or refrigerate at 40°F or below; transport with ice packs.