One Piece isn't an End Goal, No One wants to find One Piece & then Retire lol
Every Character have their own Personal Dream & One Piece represents your Best Shot at achieving such Goal
We already got Confirmation that Roger & Luffy did indeed have Personal Dreams beyond finding One Piece
It's just that They believe if Finishing Grand Line Journey doesn't Fulfill their Dream, then Nothing can
Big Mom also have a Dream, it was Revealed during her Arc
Same for Kaidou & Xebec & Crocodile & Doflamingo & Law ... etc
So before talking about whether Mihawk was interested in One Piece or not, We must first discover his Personal Dream
And so far, it seems that his Dream is a Duel, as for why? We don't know
It could be a Prophecy, it could be an Offering to a God, it could so that He can reveal his Hidden Power, it could be to Fulfill a Promise ... etc
So Mihawk was interested in those with Great Willpower, Great Ambition & Great Fame, cuz Highest Chance is that his Dream Opponent is among them, but finding One Piece himself wouldn't get him closer to his Dream at all
Mihawk is basically a Major Player in One Piece League, but He was only one whose Interest lies solely in the Players themselves rather than winning the Cup itself