Using Sanji as an example of how Oda could treat Shanks. I’d wager it’s possible he has a griffin sword, but he surely isn’t reliant on it.
Rather, much like Sanji, Shanks probably just uses the Griffin to enhance his own Roger-based fighting style.
One thing that would fit really well: the Griffin’s power lets Shanks teleport or move at super speed. This allowed him to blitz Kid, save Koby, and threaten GB all from miles away.