Not in the Age of Grace.
From my experience, young ones from 2-5, generally will break their will at any form of capital punishment, no matter how lightly applied. It manifests how closely we desire to promote our freewill. When it is violated, that hurts more than the switch.
Now some kids are more rebellious and strong willed than others. They might require the switch.
Usually, mandating they go choose the switch, puts them in a dilemma. Choose one that is soft, and get it swung twice as hard. Choose one that is rigid, and suffer the strokes.
The intent is to give Mom enough time to prepare for the administration of the Board of Education to the Seat of Justice, as much as it is for the young one to ponder their impending discipline.
The root of the problem is a thinking issue. Just swatting them might help capture their attention, but the purpose of the punishment also serves to get the young one to reconsider and think about how to avoid the punishment in the future. It is a powerful incentive.
The best defense for the father is to ask the young one if they would commit their vice again, after their punishment. If not, then it likely worked. If they do, then swat them again, with an extra stroke for not learning the first time.
How do you lightly apply capital punishment?
Nonsense, demonstrably false nonsense and cruel. I don’t know what you mean by “Age of Grace”, but there isn’t a need to hit a child for correction, ever. Well, unless the hit itself is to spare the child from further harm as in tackling someone to prevent a bullet hitting them.
You wouldn’t hit an adult. Why can you get away with it for small children? Because they’re small and vulnerable.