I’ve seen very few references to school CP using hand spanking and I think the reason is obvious – it involves the teacher touching, whereas with an implement it’s the object which is touching the pupil. I doubt whether hand spanking would have been featured as an acceptable mode of CP if local guidelines were in place, having said that a female junior or infant school teacher would probably have been safe issuing a smacked bottom in my childhood (the 1960s) but if you’re talking male teachers and girls of secondary school age even in those innocent days someone would no doubt have questioned it, to put it mildly.
Being in loco parentis doesn’t give ALL the rights of a parent!