Slow Cooker: Place the chicken breasts, diced onion, 1 diced celery stalk, minced garlic, and the chicken broth in the slow cooker so the chicken is mostly covered.
Cover and cook on high for 4 hours, until the chicken is cooked through and tender.
Remove the chicken to a cutting board and reserve 1/2 cup of the cooking liquid; discard the rest of the liquid in the pot.
Shred the chicken with two forks, return it to the slow cooker with 1/4 to 1/2 cup of the reserved broth and the 1/2 cup cayenne pepper sauce, and heat on high for 30 minutes to meld flavors.
Instant Pot option: Combine chicken, diced onion, 1 diced celery stalk, minced garlic, and enough broth to mostly cover the chicken. Seal and cook on high pressure for 15 minutes, then allow a natural release.
Remove the chicken, reserve 1/2 cup broth, discard the rest, shred the chicken with two forks, return the shredded chicken to the pot with 1/4 to 1/2 cup reserved broth and the cayenne pepper sauce, and sauté 2–3 minutes to combine.
To assemble: Spoon about 1/2 cup of the buffalo chicken into each lettuce leaf, top each with about 1/4 cup shredded carrots and a few celery matchsticks, and add dressing of your choice if desired.
Wrap or fold the lettuce leaves around the filling and serve immediately.