In a slow cooker, place the chicken breasts and thighs, wing sauce and stock. Set to low and cook until the chicken pulls apart with a fork, 6 hours.
Remove the chicken and drain off any excess liquid, reserving the liquid for a later use. Shred the meat with two forks and then chop until quite fine. Mix the chopped chicken with the blue cheese, carrots and celery. Add the melted butter and hot sauce to taste. Add about 1/4-cup drained cooking liquid back to the mix to moisten.
Cut off the tops of each tomato and scoop out interior with a small spoon. Stuff each hollowed-out tomato with a scoop of the chicken mixture.
If desired, warm up slightly in a 300 degree F oven for 8 to 10 minutes. Serve with a dipper of your favorite ranch dressing, carrot sticks and celery sticks.