Stir together chicken, hot sauce, and melted butter in a large bowl until coated.
Mix in cream cheese, shredded cheese, blue cheese, celery, green onions, garlic powder, onion powder, salt, and pepper.
Warm oil in a deep skillet to about 350°F. Keep wrappers under a damp towel so they don’t dry out.
Place a wrapper like a diamond. Spoon about 1/4 cup filling near the bottom corner.
Roll up halfway, fold sides over, brush top edge with water, and roll tight to seal. Repeat with remaining wrappers.
Fry egg rolls in batches until deep golden, 2–3 minutes per side. Do not crowd the pan.
Drain on a wire rack or paper towels. Rest 3 minutes, then serve with dressing.