A quick and slightly dirty ...

[Ursa major]

mgir, I simply don't see the difference.

The fact that Dee says "What pistol" informs the reader that Dee has tried to hide it. The rest simply tells the reader when, how and from where Dee obtains the gun.

So the difference is that the original sentence tells two things (one of which has already been shown); the changed version shows one thing and tells the other.

 

[Asmer20]

We don't need to know that he was trying to cover up. You're showing it, so why feel the need to tell it, too?

“What pistol?” said Dee trying to cover up that when Barrett had gone to warm up the engines, he’d cracked the code in the trunk and snatched a piece that’d pleased his eye.

compare with

“What pistol?” said Dee. When Barrett had gone to warm up the engines, Dee had cracked the code on the trunk and snatched the first piece he took a fancy to.

If you use the second sentence, be careful to point out that Dee did the thing, otherwise it made me think that Barrett snatched the weapon.