Sengoku and Mihawk will probably have some cling-clang equal clashes together where Sengoku is maybe the one sweating and huffing more cause of his old age, like in Rayleigh vs Kizaru. Mihawk will probably look nonchalant or something during the fight.
Croc or Buggy will somehow pull off some trick like a hostage situation or whatnot to distract Sengoku or render him vulnerable, allowing Mihawk the win. If Buggy is responsible for it, then Mihawk will comedically have him beat him up again for interfering in his fight.
This way, he preserves Mihawk's hype so he won't show his full bag during the fight and gives his fans a way to say he wasn't going all out. While Sengoku gets his respect due to being an old man who lost only due to outside intervention/dirty trick.