Good job you just admitted Mihawk>Shanks.
Just like you said Skills, CoA, CoC, physical power etc. they are all included in swordsmanship.
So when Mihawk is stated a better swordsman than Shanks, that includes conquerors haki, and all the other combat abilities you listed.
Meaning in a fight where all of those things are taken into consideration, Mihawk wins π
Good job Worstgen