Why do you assume Shanks and Mihawk didn't fight purely with sword skills? Nothing else is ever mentioned. However I think the opposite, that they only used their sword skills, might have been mentioned (not sure). If it were different, it would also completely eliminate any uncertainty about Mihawk's status compared to the Yonko. (People have only started saying he is basically on par with the Yonko recently, by the way, and basically just because. I'm not saying it is not plausible, but the manga left that open.)
And it would arguably diminish Shanks somewhat... And by the way, Vista would be Shanks-level too now. (Just another joke about being too certain about the pure plausibility of a string of conclusions.)
It is actually the first time I have ever seen someone state definitely that Shanks used his full capabilities rather than his sword abilities and strength, of course. And by the way, would Mihawk even care about "dueling" with him then? I think not.
What "Oda's definition"? No, he would only beat him as the "better swordsman", if the meteor would somehow be channeled in his sword... In other words, he would actually have to use his sword. Otherwise it's nonsense, and you could just say just about all Yonko are the WSS, end of story, move on... Your "definition" is arbitrary and doesn't make sense, even by what others have allowed.
Edit: I see you used the next line to say something about that, however I still think it's not accurate, for two reasons: 1. Maybe he could deliver the final blow to him when he's basically already down with something else, however he would basically have to be brought to defeat in a sword fight mainly. Otherwise talking about a sword fight would fall apart. Delivering the "final blow" in turn then is just a formality to not be overly pedantic, because this would also let fall things apart in making them too artificial.
2. Talk of different types or degrees of swordsmen was already introduced, so someone who uses more mixed techniques, depending on their power (proportion of damage) and independence, could possibly not deserve that title. It would have to be seen.
(And I would add someone with the title "World's Strongest Swordsman" likely aims to overcome any challenges with his sword-fighting skills alone, or else the title itself - whether one finds one can somehow call someone a "swordsman" or not - becomes a bit sillier.)