Obviously some ta'veren effect helped in bringing up this sword. This indicates a certain significance. I think the best idea to explain the new found sword is indeed that it is Hawking's sword Justice. This sword could come into play, if Rand finally meets the Seanchan. Maybe the Seanchan have a certain Prophecy about this sword or Rand will give it to Tuon, because it's basically an imperial regalia.

This could be connected to Egwene's Dream in CoT about the Seanchan woman, who has a sword:
"Suddenly a woman appeared, clambering down the sheer side of the cliff out of the clouds, making her way as deftly as if she were walking down stairs. There was a sword strapped to her back. Her face wavered, never settling clearly, but the sword seemed as solid as the stone. The woman reached Egwene's level and held out one hand. 'We can reach the top together,' she said in a familiar drawling accent."

If the idea is right that Rand will give it to the Seanchan while making an alliance, Egwene's Dream would imply that Rand and the Seanchan are already allies, when the Seanchan attack the WT. Maybe Rand will support the attack on the WT, if he learns from Semirhage that Mesaana is in the WT and that Egwene is a prisoner there.