Cook chicken: In 12-inch skillet, heat oil over medium-high heat. Add chicken tenders and cook 4 to 5 minutes or until chicken loses its pink color throughout and internal temperature reaches 145 degrees F. Transfer chicken to cutting board; cut into 1/2 inch pieces or slightly shred. Return chicken to skillet over medium heat. Stir in wing sauce and heat through, 2 or 3 minutes.
Meanwhile, preheat broiler with oven rack about 6 inches from broiler.
Make dressing: In small bowl, mix together well ranch dressing, mayo, and blue cheese. Stir in diced celery until well blended.
Prepare buns: slice tops off buns gently and set tops aside. Place bottoms on broil pan or rimmed baking pan WITH SIDES TOUCHING.
Assemble sandwiches: top each bun with 1/4 cup or so chicken mixture. Top chicken with rounded tablespoon blue cheese mixture and 1 square cheddar slice.
Broil sandwiches about 1 minute, watching carefully, or until cheese melts.
Serve: Remove from oven, put tops on sandwiches, and use a spatula to serve (hot!)