So Mach Tuck after hearing what we would do are you ready to put down the gun and pay for cable?
I would say to the gunman:* “Have you had ever heard of the horror of blimps?*”
roflmao 
ONE prop? My juggling act wouldn’t be nearly as impressive as it otherwise might have been…
I would probably start singing in Irish. Most people have never heard the language before, so they listen hard and long trying to figure it out. My sad American accent helps to keep even the most accomplished Gaeilgeoir guessing. 
My prop is the Kensington Runestone. My talent is to explain to him in as much detail as I am capable of, the history of the thing. Entertaining? Perhaps not…but people need to know. They need to know, and that may be my last chance to tell. Plus I can’t sing and he said no sex.
Sing. My voice could scare Satan.
Or recite my poetry.But since a lot of my poems are about terrorists, the person with the gun might try to recruit me into whatever criminal syndicate he was running.
my prop would be an apple in the Annie Oakley tradition.
When I was sitting in the theatre watching the movie The Aristocrats, I was thinking about how* I* would tell that joke when it occured to me that I didn’t need to make something up, I could just riff on a true life story from the ER involving a surgeon, an apple, an inmate from the local hospital for the criminally insane and an orofice you don’t usually think of apples going into.
This scenario is reminiscent of a Goodfellas scene, featuring the old meme of making someone dance by harmlessly shooting bullets at his foot zone …until Joe Pesci subverts this meme by actually maiming one foot.
For a prop I’d choose a long book like The Stand and read it out loud from beginning to end.
I’ll predict the newspaper headline for this date in 2020. We’ll meet back here then, and you can shoot me if I’m wrong.
I’d mock him until he developed an eating disorder.
Absolutely and totally off-topic, but your comment compels me to ask: Do you know Professor Mark VanStone?
We now suggest prunes to return you to your regular program.
I’d actually like to change my answer to “better nate than lever!”
The more I think about it, the more I really don’t like the no sex rule.
My prop would be a very, very thick tome on how to perform hypnotism. And I’d study it, and then practice it on him, trying desperately to make him think he’s a super nice guy who would never want to hurt even a fly every time he considered killing me.
If that didn’t work, I’d just hit him over the head with the book.
I would do my impression of Jesse Owens. 
My children tell me I’m a fabulous performer of the book “The Monster at the End of this Book” starring lovable, furry old Grover. I would have to hope that five minutes of entertainment would grant me a stay of execution.
About all I can do entertaining is make fart sounds with my hand and underarm.