Hakai is a CoC attack. It’s name in japanese is 覇海, and Conquerors Haki is 覇王色の覇気. Both share the 覇 kanji, which means supremecy. CoC users are known as 覇王, (Supreme Rulers), again, 覇 kanji used.
Big Mom’s Ikkoku doesn’t use it- it’s 威国 in Japanese, but Dorry and Brogy do seem to be using it and it wouldn’t be a surprise if they were CoC users, since their attack name is 覇国. Again, the 覇 kanji, supremacy, colour of the Supreme King.