Slow cooker method: Place the chicken breasts, diced onion, 1 stalk diced celery, minced garlic, and chicken broth into the slow cooker, adding extra water if needed to cover the chicken.
Cover and cook on high for 4 hours.
Remove the chicken and reserve 1/2 cup of the cooking liquid; discard the remaining liquid.
Shred the chicken with two forks, return it to the slow cooker with 1/4–1/2 cup reserved broth and 1/2 cup cayenne pepper sauce, and cook on high for an additional 30 minutes to meld flavors.
Instant Pot method: Place chicken, diced onion, 1 stalk diced celery, minced garlic, and chicken broth in the Instant Pot, adding water if needed to cover the chicken.
Cook at high pressure for 15 minutes, then allow a natural release.
Remove the chicken and reserve 1/2 cup of the cooking liquid; discard the rest. Shred the chicken with two forks, return it to the pot with 1/4–1/2 cup reserved broth and 1/2 cup cayenne pepper sauce, and sauté or simmer 2–3 minutes to combine.
To assemble wraps: Spoon about 1/2 cup of the buffalo chicken into each lettuce leaf, top with about 1/4 cup shredded carrots and some celery matchsticks, add dressing if desired, then wrap and serve.