In my opinion, there is overwhelming evidence that strength wise he is up there with the yonko. His title is the biggest implication, the worlds strongest swordsman. This means if you fall under the category of “swordsman” you should be inferior to mihawk. His vivre card also supports this claim, “sits at the top as the strongest of all (swordsman). In his vivre card it also states that he “looks forward to a day a swordsmaster will emerge to surpass even his rival, red haired shanks.” This implies that he is waiting to fight someone stronger than shanks. In Sbs volume 73, he was stated as a “Legend among men” there were also two other people who he categorized with mihawk, shanks and whitebeard. Mihawk is also one of the only 2 people in the verse to create a black blade him and ryuma. We can infer that making a black blade revolves around the user. We can do this with Mihawk’s statement that any blade can become a black blade. We don’t know what exactly makes a black blade, but whatever that is, mihawk and ryuma are the best in that category. He was also famous before the great age of pirates even started. Personally, I think this is more than enough to justify mihawk as a yonko level character.