I can only state on the position in England at this time. Most Schools and Education Bodies had rules concerning who could administer corporal punishment.
They had to have this consent in writing.
The trouble was, that most only regarded the cane as corporal punishment at this time.
The use of the slipper and certainly the hand did not come under this restriction.
Indeed at that time if a teacher caned who was not in authority to do so it was a matter for the school rather than the police.
In most cases, the school just stated and gave the teacher the authority. In others, they were just warned about future conduct.