I would leave it alone and cherish it the way it is. Your Grandpa sounds like one heck of a guy, you know best. This shotgun was important to him as he never replaced it with something " new and improved" . It was used by him every year, it has " him" all over it and all through out it . In my opinion, by turning this gun back into out of the box condition, you are wiping away all that family history. He didn't pass along a monkey wrench, or a chain saw. He passed along a very special hunting tool, his very personal shotgun, that gave him pleasure every year, a lot of his life. He might have nearly wore out the mechanism, beat up the stock and forearm, wore and scratched the bluing for all those years and left it in the fields and marshes, spec by spec. Varnish too, maybe even splinters of walnut here and there. And he wanted you to have it, and have it just the way it is. He didn't have it restored to give it to you, he gave it the way it is. If you inherited it to you after his death, without his will stating it, his presence still gave it to you. You got it for a reason, his reason. Look at that gun and picture it all pristine, then ask yourself if you would enjoy your Pappa's gun that way. Would it really look grand? or would it simply look like a pristine shotgun your Grandpa owned. Will you initially like the gun all shiny and new, but then suddenly feel something wrong and ask yourself " what have I done? " Remember, once it's restored, it can't go back. One more thing to ask yourself, and only you know the man. What would your Grand Pa do?
Concerning the Corvette. Great cars were meant to be restored, not let fall apart. Shotguns earn their place by use, not being locked up in a cabinet their whole life and admired and polished like a piece of furniture. A man with an old shotgun in pristine condition has little memories, a man with a beater, will pass with a solid smile on his face.