Even if you gave them your keys, I doubt that they will keep you alive. Cause they already got what they want, so what's the point of keeping you alive? Once they can have access to your Bitcoin, it means that they'll have enough money to protect themselves even if they kill you. They're bad guys so how can you trust them to keep you alive after giving them your Bitcoin?
I've read a case few years where a rich bitcoin investor who showed off driving expensive cars and living in apartments disappeared. They found his car parked and from what the police had found he probably drove off with someone in that person's car, but there were no witnesses, only tire marks. They never found his body and it's been years, so probably they tortured him to get his bitcoin and then killed him to avoid being recognized. Most likely these were people he knew because from the looks of it he parked his car and got out to talk to them.
Anyway, I can't say what I'd do. It's easy to say that I wouldn't give them my money, but what if they started to torture me. After a few hours I'd be to tired to resist them. The only thing is that I don't have my bitcoin with me and I can't access it from anywhere, so they'd have to take me home and there are cameras so it wouldn't be easy for them. Either use multisig, or hold your hardware wallet in a bank deposit box. Make it impossible for them to get it from you and you'll have a chance to survive it.