No, it's actually Zorro. There's numerous stories where Zorro is mentioned.
I remember a LEGENDS OF THE DARK KNIGHT tale where Bruce mentioned to Alfred (after acting like a flamboyant a-hole with the press), that it's an act to keep people away from the truth, something Zorro would do.
To which Alfred kinda smirked, "Your taking lessons from a fictional character, sir?"
So, in terms of who Bruce looked up to....the BTAS replaced Zorro with Grey Ghost. Bruce was a Zorro fanboy. Don't think I've ever heard heard of him being a Shadow fanboy, but I am aware of the inspiration he's taken from him- although I don't think it's as much as he took from Zorro. But, things might have changed since most people might not know who the Shadow is anymore.