My first thought was that the sfx refer to Yoru, not necessarily Mihawk, but she doesn't appear to have Yoru so maybe it really is her lineage?
Which would make Mihawk the kid brother of a non-aging old lady! Weird.
This is the kind of shit I would completely ignore if it was any other mangaka, but oda is a completely crazy person, one of the only people i'm aware of that's anywhere near as nuts as I am. So I think this is probably going to end up being important.
If Mihawk was taken in as a kid to be raised as a God's Knight, it's possible either Candel or Gunko taught him sword play.
If this is the case, we have a legitimate line between Brook and Mihawk, when it comes to learning sword play, which I think would be really cool, though obviously sad.
What if Mihawk's Island is his home island that had a human hunt on it, but Mihawk survived and was recruited by the Celestial Dragons for being so hard to kill?
https://onepiece.fandom.com/wiki/Kuraigana_Island