If it's crap ... We'll tell you
Rise of the Planet of the Apes. They wouldn't even be able to tell the difference between the CGI apes and real apes.
That's an interesting question. It's not just the visuals that you have to take into account, but the subject matter (certain sci-fi would be difficult as a lot of them make use of technology we understand with out question, but some one back then may just not comprehend it's application without explanation, like computers), current audience tastes, and then in the case of existing properties, when they were released, and who owned the rights. LOTR sounds ideal at first, but The Hobbit was written in 1937, while LOTR wasn't finished until 1949, so releasing that movie at, say 1945 would probably raise the wrath of Tolkien himself. "Reboots" were not a concept they were familiar with, and it's unknown how they would react to a rerelease of King Kong so soon on the heels of the 1933 original.
For audience tastes, the 1940's were dominated by WWII, and was a very bleak time. People seemed to want something very happy to take their minds off of what was happening in the real world.
All this combined, I think I would go with Harry Potter.
Independence Day? You want to explain the concept of a computer virus to some one in the 1940s?
Here's some food for thought.