In the Epic fight between Luffy and Katakuri , Katakuri creates big donuts from where hands appear that are coated with Haki!!! It can be seen that he isn't directly in contact with them. How is it possible to clad something with haki that you are not even touching?
This effect could be the result of Katakuri awakening his Paramecia Fruit.
Katakuri has also awakened his Devil Fruit powers, enabling him to transform nearby inorganic material into mochi, enhancing the range of his attacks and using the environment to his advantage (from https://onepiece.fandom.com)
This means that the rings are also under his control and he can use Busoshoku Haki on them.