WSS means that Mihawk is the strongest when it comes to swordsmanship. Stephen Paul even said that strongest and greatest are interchangeable in this case.
Brannew’s job was to hype up Mihawk as much as possible to justify his 3.5B bounty. Why go out of his way to specify that Mihawk is only greater than Shanks when in comes to sword skill instead of just saying “Hawk Eyes exceeds even Red Hair in strength”? The latter would make Mihawk sound even more impressive and justify his high bounty even more
The problem is people are confused about his title. They think it's limited to only swordsman, but that's not the case. The databook say he's the strongest in name and reality. Not, he's thr strongest only when it comes to swordsman. The databook tells us he became the strongest by facing strong opponents. Not, by only facing swordsman.
Mihawk's title tells us he's stronger than Shanks. So the manga doesn't have to go out the way to tell us that.
The point to mentioning the swordsmanship is for us to understand why he's stronger than Shanks. Mihawk is not a DF use so he's not strong because of that power. He's strong because of his fighting skills and power which are swordsmanship.
Another way to look at it is, the manga wants us to remember the attack Shanks used against GB and and go, Mihawk can deal with that.