To offer a bit of an imperfect analogy: I stumbled across this Church while wandering around London when I was there for some business: Christ Church Greyfriars - Wikipedia. It had been bombed out during WWII. Rather than restore and rebuild, they left the shell of the walls and steeple that had survived and converted it to a public park. It struck me as a stark reminder of how crazy it must have been to live in London during that time, with daily raids, bombings, and uncertainty about whether the island would fall. I don't think that message and that feeling could have been conveyed with a rebuilt church and pictures of the destruction in some historical exhibit. It's only by standing in the ruins that you can, in the modern era as someone who did not live through the War, even begin to appreciate what that might have been like. I think that leaving the watch as-is is a bit like that.Wow! I didn't even see this before my post with this as the hypothetical. I would definitely keep it as is. If that watch got your father through WWII, I wouldn't change a thing and I'd hope it keeps you safe the way it did him.
You can't leave all the ruins as they were. Paris wouldn't be Paris if it hadn't been rebuilt after the War. Lower Manhattan wouldn't be Lower Manhattan if the rubble hadn't been cleared after 9/11. But I do think that selectively preserving some of the destruction and some of the history is important. It became real for me as I was standing in London looking at this Church. I imagine my children will feel something similar when they grow up and stand on the edge of the 9/11 Memorial in NYC. And I bet anyone who sees your watch--and who is lucky enough to hear its story as told by you--will have that same kind of feeling in a way that just cannot be replicated if the dial and hands are restored or removed and kept elsewhere.
But again, that's just my two cents. You need to do what will make YOU happy.