In a medium bowl, toss the shredded chicken with the buffalo sauce until evenly coated. If you like a milder flavor, start with 1/4 cup of sauce and adjust to taste.
Stir in the ranch dressing to create a creamy, tangy coating. Mix until the chicken looks glossy and well-seasoned.
Warm a skillet over medium heat and add the olive oil or lightly spray with cooking spray. If you’re using leftovers, you can skip to assembling the wraps.
Add the buffalo chicken mixture to the skillet just to warm through, about 2–3 minutes, stirring occasionally. This helps mellow the bite of the sauce a bit.
Warm the tortillas in a dry skillet for about 15–20 seconds on each side, or microwave them covered with a damp paper towel for 15 seconds to make them pliable.
Assemble the wraps: lay a tortilla on a plate, spread a thin layer of dressing if desired, then add a bed of lettuce, a spoonful of the buffalo chicken, celery, and shredded cheese if using.
Roll the tortilla tightly, tucking in the edges as you go. If you like, secure with a toothpick or slice the wrap in half for presentation.
Repeat with the remaining tortillas and ingredients. Serve immediately, or wrap tightly in foil for meal prep and refrigerate up to 3 days.