I absolutely love this idea. Adore Cowboy Bebop and its soundtrack, and this edit concept has actually crossed my mind before. Here are a few essentials from the CB OST that immediately come to mind.

Space Lion - a sprawling epic of the CB soundtrack, I think Vos’s Yacht where Han sees Q’ira again could use this track for both the mood and tension of the scene.

Bad Dog No Biscuits - I could see this fitting perfectly for the opening chase scene.

Tank! - this would definitely work best for an action scene, maybe even the train heist.

Cats on Mars - one of the more quirky CB tracks, I could see this working great as a theme for L3.

Blue - the ending credits song for the final episode of CB would also work really good for Solo. I think it just naturally works very well for a climactic moment.

This is me just spitballing ideas, there’s a ton of quality tracks in the show to choose from.