I’ve always thought there was a good similarity between Virginia Madsen and Stanwyck. And, yes, I do have a thing for the Madsens.
When you deal with the uniqueness of the other three, you’re going to have to focus on looks or style, since nobody is going to have both. Otherwise, all you have is a caricature at best.
I’ve seen Rob Morrow do some things that approximate aspects of Bogart.
Not in looks, but in talent I think Steve Martin could be Jimmy Cagney. He does serious drama, comedy, and is not a terrible song-and-dance man. Cagney could dance rings around Martin, but watch Steve in a Herbert Ross film and he’s pretty good.
I can see that as a stretch if it came down to a serious effort at a biopic. I spent quite some time looking at Yahoo! Images of Cagney and the only faces that tried to come to my mind were of Kenneth Branagh and Arliss Howard, neither of whom would get the essential Cagney across. Just for resemblance alone I see a little (and only a little) David Rasche and maybe a touch of Jeremy Irons.