There is no debate.
If mihawk seraphim has mihawks skill but day zoros haki
He loses to mihawk in a sword duel
The fact is the story outright says one is a superior swordsman to the world.
If mihawk seraphim has mihawk haki but no sword skill, he loses to mihawk in a sword duel too. That doesn't tell us anything lol.
You're thinking of this like if he has one, he won't have the other. But that's not the case with shanks vs mihawk at all.
Shanks could have better haki than mihawk. But mihawk still has top tier haki. And even though mihawk has better sword skill, shanks still has really good sword skill too.
So their fight is not gonna be decided by "mihawk has better x" Or "shanks has better y"
It's gonna be a combination of all things.
And If shanks has superior haki compared to mihawk than mihawks sword skill compared to shanks, shanks could win. Not saying he has or he does. Just a scenario.
Where did it ever say the outcome of their duels ?
The outcome of their duels are still unsettled. As seen by the fact that shanks asks mihawk "come to settle the score finally?" Or something like that when we see them meet first in the story.