I suspect if he tried that in the local Confederate section of the cemetery, he’d get ventilated.
I would hazard to say that shooting such an offensive scoundrel would not typically be the remedy in southern etiquette. (Unless, of course, he was defiling the grave of kin, in which case it would be appropriate.)
But horsewhipping would be culturally recognized as the appropriate remedy for something as course as tampering with sacred ground. Sadly, horse whips and the mastery of their use are far less common these days. Acceptable alternatives to horse whips do need some consideration as to their utility.