Remove tops of green onions; set aside white portion of onions. Cut green onion tops into very thin strips; place in a bowl of ice water, and set aside. Slice white portion of 3 onions; set aside. Reserve remaining onion for another use.
Position knife blade in food processor bowl; add chicken and next 6 ingredients. Process 30 seconds, stopping once to scrap down sides. Stir sliced onion into chicken mixture.
Place 1 phyllo sheet on a damp towel (keeping remaining phyllo covered). Lightly coat phyllo with cooking spray. Layer 3 phyllo sheets on first sheet, lightly coating each sheet with cooking spray. Cut phyllo stack in half lengthwise; cut stack crosswise into thirds to make 6 stacks. Keep phyllo stacks covered.
Spoon 1 tablespoon chicken mixture into center of 1 phyllo stack to within 1 1/2 inches from each end, parallel with long edge. Roll up phyllo, jellyroll fashion, starting with long side; twist 1 1/2 inches from each end. Place "firecracker," seam side down, on a baking sheet coated with cooking spray. Repeat procedure with remaining phyllo and chicken mixture.
Bake at 400° for 15 minutes or until golden. Tie each end of firecrackers with a green onion strip. Serve with hot horseradish mustard.