Any normal Mihawk enjoyer understands whether Mihawk has coc or not it wouldn't necessarily change how he does against other top tiers.

What we do know is that Mihawk is at the top of swordsmanship, and we can also infer using Zoro's swordsmanship in Wano that Haki is included in swordsmanship (outright stated for KOH to be Zoro's pinnacle of swordsmanship).

I don't understand why Shanks fans would take it as a loss or Mihawk fans as a win, whatever overall Haki combination Mihawk has he is still above all other swordsmen and naturally that includes Shanks.

Mihawk having coc or not having coc doesn't change the truth, he is in fact above Shanks (considering the title as an absolute).

And some may think it is a Mihawk downscale that he has coc and that it would have been more impressive for Mihawk to be stronger than Shanks without it, however Mihawk's other stats haven't changed.

The Clarvoyant can still have top 1 observation.

The Armament specialist can still have top 1 armament.

And naturally now, assuming that Mihawk is in fact a conqueror he can also have top 1 conquerors.

Mihawk has no real ceiling and a very well established floor (Shanks). Having coc or not won't change it, Mihawk will still be him (considering the title to be absolute).

Image unrelated.

Mihawk having coc changes absolutely nothing