Combine all ingredients in a small bowl, mixing well. With the back of the mixing spoon, mash the blue cheese into the sour cream until almost all of the lumps are gone. Chill in the refrigerator for at least 1 hour before serving.
Soak the chicken in the hot sauce in the refrigerator for at least 30 minutes. Put the flour in a pie tin and season with salt and Cajun seasoning. Remove chicken from hot sauce, shake off excess, and dredge chicken in the flour. Set on a baking rack.
Heat the butter and oil in a large skillet over medium heat. When the butter has stopped bubbling, add the chicken tenders and cook until golden and cooked through, about 3 minutes per side. Remove from the pan and drain on paper towels. Serve warm with blue cheese dipping sauce and celery pieces.