Well, Cowboy Bebop is the second most overhyped and overrated anime I know of (with the number one spot being held incontestably by Evangelion), so what they do to it is pretty much supremely irrelevant to me.

However, visually Spike Spiegel is very much like a laid-back Lupin III, and that wouldn't be a bad choice for Keanu.

Note that Keanu is a nice, reliable, non-fit-throwing actor, and directors love working with him. This is why he gets lots of nice roles. He's also not nearly so terrible an actor as people like to paint him. He just does what the director says to do. If the director doesn't want lots of emotion, he won't get it.