I saw Indy IV again with my wife this weekend. While watching it I was thinking about the first scene and what would have made me like it more. First when the Russians give the description of the box I would have made sure that they said nothing that could not be the box we saw at the end of Raiders. I would leave out the mummy bit.
Second, I would leave out the floating gunpowder. The compass he asks for would work much better here and not have that "Hey look I have a computer" feel.
I would leave out the scene where they open the box. Let the audience, and Indy think it has the Ark in it. He could even make a "Top men" reference.
I would leave out the rocket sled. It is just too Loony Tunes. This could be replaced with a Raiders style convoy scene with Indy trying to steal the crate back. He could get pushed off the truck in the fake town.
I thought about saying that the bomb shouldn't even happen but I only wanted to change the feel of the scene not too much of the content. Instead I would change the way he survives it. Let's face it, a modern audience realizes there is no way to survive an atomic weapon. But, a '50s audience did not know this. That's why I would have had him Duck and Cover. I would have had him survive it by getting under a desk. Still makes no sense but in the warped '50s Cold War logic it worked.