Hmm, well you may be right. It's never stated that it's the haki of the users. TBH I need more explanation about why the swords become black permanently.
Yeah we all do. The explanation would clear everything up.
Because if it truly is because a sword stores haki, then that would mean not all swords can turn black but that is directly contradicted by Mihawk's statement.
So then if we move to length of use then why wouldn't WB's Bisento which he used till he was in his seventies turn permanently black?
The only thing we know for sure is that swords carry the will of the users. But we don't know anything about it carrying haki.
Also from the scans, it is Zoro who has coated the sword. It is Zoro's haki which has been sent flying.