I believe corporal punishment to be a useful tool in the tool-shed when it comes to lovingly training my beautiful 3 year old boy.
For the purposes of this question, I'll just say that my style of corporal punishment is to stop what my child is doing, calmly tell them why I'm going to spank them, and then give them a strike on the rear or hand that is just light enough to be uncomfortable, then reiterate my expectation and give them a hug and a kiss.
This method has been phenomenally effective for my wife and me and we have no qualms with doing it at home or in front of friends/family that we know implement the same style of parenting. I do not, however, ever spank my kid in public or in front of strangers. Not even a flick on the hand. I don't want to embarrass him, but even more-so I'm petrified of having someone call Child Protective Services (CPS) on me because they may believe that all physical punishment points to heinous abuse back at home. I'm not ignorant to the fact that spanking has (for whatever reason) gained a bad reputation in the last decade, but I'm also not ignorant to the fact that many (most?) parents spank their kids too.
I live in a state that allows physical punishment so legally I should have no concerns, but I still find myself stuck when my child disobeys in public and I feel forced to do nothing about it until we get home (which by then it would be too late for them to associate their bad behavior with the spanking anyway). Is there a way to execute corporal punishment in public without triggering unknowing and irrational fears in strangers?
 This is not an invitation to debate as to whether or not you agree with spanking. This is asking for a best-practice guide on spanking in public. I started my question with "I believe corporal punishment to be a useful tool..." to set the precedent for any expected answers (unlike this question) :)
 Note that he initiates 90% of these hugs, and I never force affection on him. The whole "spank then hug" thing was not a planned out disciplining strategy. It just sort of happened once and now it's routine. He expects it and I think it helps him to know that the issue is over and done and daddy isn't mad anymore.
 When I say "in public" I don't mean I hop on a table and shout "TIME FOR YUR SPANKIN!!1" and then whoop on him. I would still be as subtle and discreet as possible.