It looks like a soundtrack version without sound effects does exist. Who knows how long this link will stay up, but here it is as of today.
Just gave it a listen. There's some verses I've not heard before (the one about a mountain, and your back against the wall) which was likely edited out for the police radio dialog. ("it didn't take us this long to catch dillenger"
https://www.youtube.com/watch?v=DqWyI8CTzzA
And yes it is Ray Stevens, famous for "Everything is Beautiful" and "The Streak."

You might be able to get it by downloading the DVD into your PC, but I dont know how you would remove the background noise.
I did that, but I don't know how to remove the SFX track or the language track, so it sounds like it does when watching the movie.

I was able to find it on Kaza sometime ago, but with the background noise (which I actually like), I dont know if it is still available. You might be able to get it by downloading the DVD into your PC, but I dont know how you would remove the background noise.

It's simply called "Cannonball" or "The Cannonball". It is by Ray Stevens. As for if its on CDI have no clue. I've been up and down the net searching for a version of it that doesn't have the ambient noise from the opening title to the movieand I have failed to find any.

I believe it is a Ray Stevens songI cannot remember the name.