Mihawks always wants to fight agaisnt strong people: shanks, prime WB and luffy or zoro eos (which mihawk want to be stronger than shanks). So will be very clear to think than kaido and Mihawks had fighted in the past, but really than never happened. That's because why Mihawks will be fight agaisnt one who reconized than shanks or oden are stronger than him. Of course if he doesn't can defeat these swords which are weaker than him, there are nothing reason to fight Mihawks was wasted his time with a fight that he knows will be win 100%.