Here are two conflicting answers for you, pick the one you like, both are rooted in truth:
Virtually any strings would work for that style of music in the right hands. Technique is the biggest factor, followed by setup and then your amplification signal chain. Add to that room dynamics and what you are blending with/competing with in the band. The bigger the room, the noisier the band, the less the character of your strings will come through on the gig. When that happens, to come through as "darker/warmer" in your live setting, you'd be better served with something with the opposite character in your practice room.
The second answer is that if the sole purpose of that bass is that Sinatra style project, then gut strings. Don't fall down the hole of "gut-like, hybrid options". If that hole is worth falling into (and I've certainly fallen into and climbed out of it) it is because you want that sound, but also need versatility for a variety of other situations as well.
