Shanks became an emperor decade after battling Mihawk, clown post through and through
Heehaw never defeated Shanks
Heehaw is in no position on who he considers worthy to challenge when he hunted don krieg
Shanks became a Yonko 6 years after he lost his arm. At the most it would have been 6 years. That's assuming they never fought after he lost his arm to determine Shanks is not a worthy opponent.
Mihawk is the WSS, not Shanks so he won.
When Mihawk found yonko Shanks to tell him about Luffy's first bounty Shanks thought he was there to fight and was ready. Shanks still considers him a worthy rival and was ready to go wild. Stick to the manga not two piece.
Mihawk only one after Don Krieg because he disturbed his sleep and even that he didn't even finish him off. Read and comprehend the manga.