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? Also, if other trusted family members know your Bitcoin, and you got killed by not giving it to the kidnappers, they can target your family as well. In this kind of situation where money involves, you can't be sure that you'll be safe even after giving them what they want.

The best thing to keep you and your Bitcoin safe is to keep it private. The bigger the amount, the more private you should be. No matter if it's a relative or a close friend.