At my place, you'd get a demo on you,but that's just the simple answer, not a challenge so don't go boarding Qantas. I've had this happen. Well, not the guy rolling up and saying, "Show me the power of your martial arts" Who would do that except on a late-night Kung Fu movie? But, I have had it happen, sort of.
This happened last year. No wait, this is 2017, so it was 2 years ago but we were still at the same location as now. The instructor from the TKD school literally in the same building complex came in, Korean guy, and literally asked my first student who greeted him, "Does your aikido work? I would like to see some of it." He had just stepped off of his own mat and walked down the sidewalk, in his dobok, so I was wondering... "What time is it and what channel am I tuned to right now?" Frayed & graying black belt and everything.
Long story short, I talked with the guy, and he was looking for something effective, but which would not offend the local school district's police policies on defensive violence. Right now, in most of the US it is deplorable, if a kid swings at your kid, and your kid gets hit, then hits back... both kids get sent to in-school kid jail. Sometimes, even if your kid is not hit, both kids go to the same in-school jail. So, he'd found for himself a situation where his own hard-won skillset was not really appropriate and useful and it was tearing him up.
So, I ended up using a corner of the mat and giving him some simple, non-striking things that he could quickly show his son in case of the usual types of bully attacks like the bear hug and the suckerpunch (assuming he saw it coming). Just movement based stuff and stuff anyone with: A) a clear head (he was really torn up about it); and b) some background in a grappling system... would know.
One of my buds takes his girls to a nearby judo school I'm loosely affiliated with and I pointed him at that school. He stopped by about a season later and thanked me, his son wasn't having the problems he'd been having any longer.
Accepting the challenge of "Your stuff don't work" can be done in a de-escalating manner, just like with any other type of... engagement. Attitude mostly. Like when a guy's all drunked himself out and the girl has left the bar with the other guy and all he really wants, he thinks, is to hit someone. Talking that guy off of his personal cliff is in the same family of skills.