Not.
Assuming that it is unaltered, not rusty or badly battered, nor previously refinished, it is best to leave it alone. It will have more dollar value, more collector interest, more historical significance, and I would think a closer tie to your great uncle in its original condition. My uncle was in the Army between the wars, I wish I had his pistol or other mementos.
Just clean it - no sandpaper or steel wool, please - oil it, and admire it as a chunk of history. I'd put in a fresh full strength recoil spring and buffer to shoot it. And I would shoot it, that's what it is for.