It’s not really a genre, but one of the musical niches I really dig are songs that sound like they could be the theme of a Bond movie. Usually female vocals, very dramatic sounding, maybe an orchestra.
Bjork’s Bachelorette is one of my favorites.
Caro Emerald’s I Belong To You is great too.
What have you got that fits that mood?
I think so, but I’m not sure. If you liked those, you might also enjoy Goodnight Julia. That’s the only other proper song I can think of from the Cowboy Bebop OST.