This is what I don't understand. He could have shot Audrey, which would have kept Jack off him. Either Hendersen really might have a heart, or he's just a sadistic piece of trash who is toying with Jack.
What he did was create a pressing need for Jack to actually have to rescue Audrey. That was the way to get Jack to give the tape and attend to Audrey, effectively allowing him to get the tape and get Jack sidetracked. There was no "heart" in it. Just cold logic and a sizing up of what Jack would do.