It is canon. The DMC4 special edition tin case shows a close up of Dante's gun, they have "For Tony Redgrave" ingraved into them. Dante only ever uses that name in the first novel, it's what the gun maker knows him by.
He was alluded to have used the name in the past in the DMC anime. In one of the episodes, he visits a small town where someone claims to have been childhood friends with him, referring to him by the name "Tony". Dante makes the audience and his current friends believe they have him mistaken for someone else, but the episode shows at the end that he was indeed that Tony from the past.
Also, the "FOR TONY REDGRAVE / .45 ARTWARKS" engraving has been on Dante's guns since the first DMC. "Tony" was actually Dante's name early on in development, too.
Like I said, DMC3 makes the first novel non-canon mostly, but a good majority of it isn't contradicted by DMC3 either, namely where he got the guns, his relationships with his friends in that, etc. Pretty much the plot of Gilver needs to go and it fits nicely into canon.