I'm pretty sure it's the former. Saying that it's the latter is like saying Whitebeard was the best at being a man, or that Kaido is the best at being alive.Portrayal Wise Shanks is definitely in the lead as of now.
Title wise Mihawk would make sense. Yonkou > Shichibukai BUT Mihawks title is more specific towards him and Shanks. Its not as vague.
But titles always have loopholes in them, always. Mihawk's title could easily mean Mihawk is stronger in swordsmanship, but in a full out battle he doesn't necessarily have to be the last one standing.
There are two ways to look at Mihawk's title. Strongest person who holds a sword OR Strongest in the art of swordsmanship.