Heat chicken and hot pepper sauce in a skillet over medium heat, until heated through, about 5 minutes. Stir in Neufchatel cheese and ranch dressing. Cook and stir until well blended and warm, 5 to 7 minutes. Mix in half of the shredded Cheddar cheese, then transfer mixture to a slow cooker.
Sprinkle remaining Cheddar cheese over top, cover, and cook on Low until hot and bubbly, about 30 minutes. Serve with celery sticks and crackers.
