For me personally, doing such a thing would guarantee I do not patron your business. I am not saying it doesn’t suck to have someone clearly take advantage of you, but it is the cost of doing business and many will see it as such. To me, and please note I am not saying this in reference to you, it would indicate a childish behavior unbecoming of a business professional.
Analyze it this way, what do you have to gain? The patron who took advantage of you has no intentions to pay, and will likely use the tactic as a way to say “Well I was going to pay you, until you did this,” which would only add to your frustration. So the money will still be missing. You may get a couple of sympathizers who will tell you how horrible of a person the guy must be, but at the end of the day when they leave your establishment they will likely never think of him again. You may gain a personal sense of satisfaction temporarily from the “I’ll show him” mentality initially, but it will be short lived at best once the negatives set in.
Speaking of negatives, you will likely upset several customers. They may not be vocal about it, but public shaming for something “petty” is considered beneath many people, especially business owners, and unlike the few sympathizers you may gain these people will surely talk about their disgust with others, not in the person you picture but in your business. It is likely that some customers may choose to no longer patronize your establishment, and encourage others to do the same, perhaps out of fear that they will do something to end up on your “Wall of Shame”, or maybe just in simple disagreement with the tactic. Perhaps worst of all, after all is said and done you will not have your money back, nor will you have won your battle on principle.
Me personally, I would file a police report on the individual for theft, because at the end of the day that is what he did.
Hope my opinon helps in your decision.