Fair enough. There's no reason to not think he didn't get the swords from his master. I personally never thought much about them and took them for generic weapons.
Another thing to remember is that it's possible that the 2 swords we see in the Kozaburo flashback might not be the same ones that broke in the Baratie. He'd told Mihawk he'd broken multiple swords in his lifetime - including the two during their duel - not that those swords were the only ones he'd ever broken.