Probably tell Carl Hanratty’s joke from Catch Me If You Can, which is in the running for top twenty jokes ever.
Knock knock.
Who’s there?
…
…
…
Go fuck yourself.
Same here my friend, same here… 
Ha, my thought exactly.
Some fun answers here. But I’m starting to think that shaggy dog stories may be the way to go. Even if he shoots you afterward, you bought yourself a fair amount of time!
I could dance. I could sing, but then I’d just get shot.
No one has said they’d try to seduce him with a sexy dance? Dunno if it would work, though, but technically it is entertaining.
Well, I hope the gun-man likes story time, because I certainly have a fair-to-middling amount of what have been called entertaining personal stories. I can sing decent too, but I can’t play guitar so it might suck royally without instrumentation. Although, I can do a not-half-bad ‘Over the Rainbow.’ Although squared, that could lead the situation from bad to worse ba-dum-tish
I said no sex, meaning actual sex. A sexy dance is entertainment, and therefore permitted as long as it has artistic merit.
Please send me videos of such if there are further questions, and I will provide guidance. 
My one prop is a loaded gun.
Well, I was a professional storyteller for a while, so maybe I could, like Scherezade, keep him listening until someone could rescue me.
I would sing this.(You Tube)
I would have to join you as a reverse drag Dr Scott, at least I actually have spike heels [somewhere] fishnets [also somewhere] a plaid stadium blanket [um, somewhere] and a wheelchair. Although I used to do Janet, I could probably get it sorted out reasonably well.
I guess being a gimp does come in handy
IRl I do not handle ultimatums very well. I would tell him to go fuck himself.
I do my Ozzy Osbourne impression. My fake Brummie accent is brilliant I tell ya.
SHARRRRRONNNNNNN!
Sing and play guitar. In this circumstance, mostly lullabys. Maybe some Coldplay.
The OP said “no sex”.
I’d probably go with poetry recitation. Jokes have the potential to be better, but they also have a much greater potential to be much worse. At the very least, people seem to be impressed by the fact that I actually memorize poems (it’s really not as hard as most folks think).
That’s not sex, it’s masturbation.
Right?
“Don’t knock masturbation. It’s sex with someone I love.” – Woody Allen
I tend to tell myself bad jokes when I get really deathly afraid, so I’d probably be doing an impromptu stand-up routine anyway. Death will be swift.
Alternately:
“Hey, look over there!”
Tim Allen (of Home Improvement fame) claims to have avoided getting beat up/killed in prison because he was funny. Seems some guy had him up against the wall and, for reasons he could never explain, Tim started doing Elmer Fudd impersonations to make the guy laugh.