I think the title of World Strongest swordman exists in the common world ( world in control of WG) from the time of Ryuma. I believe that the first WSS is Cyrano, the antagonist who destroyed villages in Monsters!.
Why I am saying the first WSS is Cyrano?
It is stated that Cyrano is a strong swordsman and second only to the sword god himself. After that time, the title was held by many warriors and Rayleigh may be the previous wielder.
Why Mihawk now?
I believe it was Mihawk life long dream to be WSS, he became one after a long and difficult journey. He became WSS to pay his own respect to Cyrano, who I belive is Mihawk's ancestor as Ryuma is for Zoro. If u read monsters you could identify the similarity
In future, Mihawk and Zoro clash will be similar to that of the captain Haddock and Saccharine in Tintin movie.