First of all, Mihawk never attempted to cut diamond for us to assume he can't cut it. Mihawk seemingly wasn't even trying when he initiated his attack, Yet it took the man with hardest defense at MF to block his attack. Further, the attack was one handed slash when it's quite evident that Mihawk uses both the hands which should logically increase the power output by at least two fold. The most ridiculous part in your theory is that you think Shiryu who by portrayal is far weaker than Mihawk and also a swordsman can somehow bypass Jozu's diamond defense and kill him. But, Mihawk of all people couldn't cut through the same shit.
Another thing people needs to realize is that Shiryu displayed no interest in being WSSM. Therefore, there is no reason to believe that he'd go after Mihawk and they gain literally nothing by attacking or fighting Mihawk. Why because even if Shiryu kills Mihawk thanks to diamond fruit, it still doesn't make him the strongest swordsman since he didn't win the battle because of his skill as a swordsman. Mihawk is up there with top tiers of the world which includes people like Shanks,Blackbeard and even Kaido. So, if Mihawk can't beat a diamond fruit user, same applies to most of the top tiers which doesn't make any sense to began with. Not to mention being superior to Mihawk'd kind of put Shiryu on the same level as BB who's reserved for Luffy. As far as I remember there wasn't a time when Zoro's opponent is on the same level as Luffy's in terms of power.
EDIT: I know being a devils fruit user doesn't stop one from being a swordsman but there is a clear difference b/w using your ability in conjunction with yours swordsmanship akin to what people like Law and Fujitora'd do and your the hardness of your body to your advantage. It may make him stronger than Mihawk but it won't be different from Mihawk getting defeated by someone like Kaido or Whitebeard.
As you say we can't know he can't cut diamond because he didn't try, Jozu taking the attack doesn't mean the man with the hardest attack was needed to block it. Mihawk could theoretically cut diamond if he tried, WB theoretically could have stopped that slash if he tried, we can never know. Just playing devil's advocate.
His theory never said the fight had to be 1v1 from start to end and Shiliew has BB to steal DF powers away.
No reason? Not even say BB Pirates betray the WG try to take over and WG sends out Shichibukai and Admiral to stop them and yes they would send them as well, BB's a yonkou and they called in everyone when one Yonkou threatened them already if another did it using the first one's power plus his own of course they're gonna call in all their guns.
You say if he beats him with the fruit it won't matter because it's not pure swordsmanship so he won't get the title but you say earlier he doesn't want the title so which is it? Also if he doesn't want the title then he'll have no apprehensions about beating him with the fruit.
Just because Mihawk can't(theoretically) beat a diamond user doesn't mean the other top tiers couldn't just because he can compete with them. Say Mihawk can't cut Jozu, BB can take his Diamond armor away, Shanks con focus his Conq. Haki at jozu and wear him down if not KO him with a focused attack. That argument doesn't even make sense "these guys are close in power with completely different fighting styles, if guy A can't beat him none of them have much of a chance"
Not saying his theory will happen exactly as he's laid it out but you're reasons against it are all fairly weak.
