Hi Justin,
Given modern molecular technology, it would be possible to find human DNA on a sword with little difficulty--if it's there to be detected (i.e. the blade hasn't been cleaned recently.
That said, in most cases, I would suspect that any human DNA found on a blade would belong to its current owner. Remember, we shed hair and skin flakes fairly constantly, and some of that will get stuck on any sword kept out for display or used (for practice or whatever).
You could also try swabbing the inside of a scabbard, or cutting it apart for samples, if you want to get carried away. You might find traces there.
Given the cost of such tests, I think this is a waste of money and time. But if you're curious enough...
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