Preheat the oven to 450°F and line a baking sheet with parchment paper. Thread the chicken strips onto 6-inch bamboo skewers, 1 or 2 pieces of chicken per skewer.
Combine the hot sauce, butter, vinegar, grated garlic and a pinch of salt in a glass measuring cup. Microwave on high until the butter is melted, about 30 seconds. Stir together to combine.
Dip each skewer into the hot sauce mixture so that the chicken is fully coated, then arrange in a single layer on the lined baking sheet. Bake in the oven until sizzling, about 5 minutes.
While the skewers are baking, stir together the yogurt and blue cheese; season with salt to taste. Remove the skewers from the oven and serve immediately with the blue cheese dip and celery and carrot sticks.