He used a sword to battle off Rock Pirates lately, and we watched him do so. During their final battle, he used one on Whitebeard as well.
Upon reflection, I found Roger’s sword to be strikingly similar to the one wielded by Gryphon in Shanks’ story.
While Whitebeard’s Murakumogiri naginata shattered the sky with its power, Gryphon’s durability and tenacity make it an equal opponent.
It was powerful enough to deflect Sakazuki’s magma fist when imbued with Haki.
So, unless Shanks has a sword that is almost identical, I’m going to assume they are the same thing. So both Gryphon and the straw hat belonged to Gol D. Roger at one point?