Well, as everyone else says, it boils down to what your gonna do with it. If your not going to sell it, and if your not sentimental about the patina (which, by the way, is a perfectly valid thing to consider), then have it reblued. Spend the necessary money to have it done by someone who knows what they are doing for 2 reasons: One, you can be assured of a good job, and two, they will treat it with respect both historically and personally. Lots of people can refinish a gun perfectly well, but this isn't a new 1911 or something, this is a gun that clearly means something to you and as such, you should spend as much as you can afford to insure a job done properly. Put another way, if this were just some pawnshop special, I wouldn't worry about the rebluing that much. It's not, so you should.
If you think you ever might sell it, don't refinish it. Even with the worn down finish, it is worth more in it's current state than it would be reblued.
If it were me, I would probably leave it just as it is. It might require a little extra effort on your part to keep the rust off, but it requires no effort on your part to hold it and think about your grandpa. As someone else mentioned, Grandpa's hands wore it down, and rebluing is just going to erase the physical reminders of him from the gun.
I would add that I have my Dads first rifle, which is also a pre-64. His is in excellent condition, but he made it clear to me that if I wanted to hunt with it and shoot it up, I should feel free to do so. I will, and I have a little bit, but the fact is that there is no good reason for me to take it out in inclement weather. I have other guns that can get wet that don't have nearly the sentimental value that this rifle has for me.