Mickey:

May I take your grandfather's point of view? I have a step-son. He has a son. Obviously we are not related by blood, but they are my family.

If that feeling is sufficiently mutual---if my grandson considers himself part of my family---then my tartan is his tartan. If he wants to wear it, he doesn't have to perform any mental gymnastics to say he's honoring me. We are not a genealogical society, we are a family. I would indeed be honored and humbled if that came to pass, but that isn't the point.

That tartan does not match either of our last names, but it's still ours.

Back to your family: From how you feel about your grandfather, it's pretty obvious that he considered you part of his family. I'd bet you a pint of the best that he never introduced you as "my step-grandson, Mickey."

Wear it, and don't over-complicate this. He's your grandfather.