You have to read chapters 561-563 again for the postponement context.
In 561, the Pacifista Army is deployed.
In 562, Sengoku made it clear that the Pacifista Army is ordered to wipe out the front of the Plqza and even WB said Sengoku was not above sacrificing his own forces. This means Mihawk could have surmised that it was to both their advantage to postpone the match lest they arrive at the Pacifistas' crosshairs. Stopping the fight indeed benefited both of them.
Also, 562 ended with Squardo stabbing WB, whereas 563 started with the reactions to that: Shichibukais (including Mihawk) and the Marines were not surprised. The pirates (including Vista) were.
In 563, WB also admitted that Akainu tricking Squardo was Sengoku's plan all along, which means that Sengoku was one step ahead of the pirates in terms of strategy. I can reasonably conclude that Mihawk and all the other Warlords were let in on the plan from the beginning.
Imagine if Mihawk and Vista were still dueling when Squardo stabbed WB. Vista would have been too shocked to continue and Mihawk would have unfairly dunked him, which we can agree is not the kind of W someone like the WSS would want. So, stopping the fight was to Vista's benefit after all.
Seriously, Posthawk bs is the most taken out of context moment in the whole fandom.