It was already said that Shanks and Mihawk always fought to a draw and they haven't fought each other in 12 years. Shanks isn't a real swordsman either. A real swordsman uses actual sword techniques and lives by the sword.
You can't have swords on your jolly roger, hold a sword yourself since your youth, use it as your main weapon everytime we see you, have "legendary" battles and rivarly with a master swordsman(who ends up being world wide known as the world strongest) while not being a swordsman yourself.
It would totally shit on your rivarly and make you wonder why exactly someone like Mihawk who is only interested by swordsmen would be interested by someone like Shanks to the point of having "legendary" battles with him.
Shanks even implied when talking to Whitebeard that he received multiple injuries during his fights against Mihawk when Mihawk has no scar on him, so i'm not even sure where it's mentioned he never lost to Mihawk