I'm not sure how you went from point a to point b.It would be a lot more effective without the hitting part. And look how you've described it .... "it is more the embarrassment than the actual swat." How do you think the child internalizes that embarrassment from being physically hit? You should listen to what other posters learned by being punished in this manner as a child - none of it was positive. And all available empirical evidence backs that up.
You don't seriously think it's not "hitting" if you use a weapon instead of your hand, do you?
The world will not spank them. And if they do, it's considered a crime.
Were you hit when you were a child?