Spray a baking pan with cooking spray and set aside. Mix corn syrup, granulated sugar, and 2 tbsp. water in a 4-qt. pot. Bring to a boil; boil 2 minutes.
Reduce heat to medium-high, add nuts, and cook, stirring continuously; syrup will crystallize into sugar around nuts and become very sandy. Keep cooking and stirring until sugar starts to melt again and caramelize, about 5 minutes. When nuts smell toasted and all sugar has caramelized and is medium brown, remove from heat. Stir in butter. Carefully pour hot nuts onto prepared baking pan (reserve pot).
Spray tines of 2 forks with cooking spray. Using forks, stir and separate nuts until cool. Freeze nuts on pan 30 minutes.
Meanwhile, add 3 in. water to reserved pot; bring to a boil. Remove from heat. Put chocolate in a medium metal bowl and set bowl over pot. Let sit, stirring occasionally, until chocolate is melted.
Transfer nuts from freezer to a medium bowl. Pour half the melted chocolate over nuts; stir well to coat. Return nuts to baking sheet, spreading out and separating them. Return nuts to freezer until chocolate has set, about 20 minutes. Repeat with remaining melted chocolate.
Divide nuts between 2 bowls. Sift cocoa over first bowl, tossing gently to coat nuts. Repeat with second bowl, using powdered sugar instead of cocoa. Store nuts separately in airtight containers up to 2 weeks.
Note: Nutritional analysis is per 1/4-cup serving.