If he had CoC, it would have been shown in Marineford and he would have damaged Jozu
You really think Mihawk put his all into that attack?
Bro was standing and threw a slash like zoro threw an attack at magistrate and cut him. It was not even named.
Bro didn't use a single named attack and Didn't bother to use haki as well.
Whitebeard himself didn't use adcoc or even coc in marineford becuz back then it was still a foreign Concept to us.
randomly Mihawk Throwing Adcoc attacks in Marineford would have Sliced marineford in the beginning only.
And for whitebeard to remember mihawk as someone as a rival of shanks and shanks actually accepting him as a rival is also more than enough to tell he has coc. and adcoc too. and we saw how great of power boost it is for Swordsman. Oden , Zoro , Rogers. There's no way Mihawk doesn't have it.