I have to say that I don’t think even the across-the-palm method would have enabled the teacher to hold the pupil’s wrist to keep their hand in place. Surely unless the teacher had a vast ape index (climber’s term implying extremely long arms it would then be impossible to wield the tawse correctly, given its length, about 21 inches. I’m surprised to hear that this was how the cane was used at your school, as a cane would normally be even longer than a tawse.
I’ve seen the ‘holding wrist’ method used with rulers, but as I’ve never seen either a cane or a tawse used on the hand I’m perhaps overlooking something in saying it would be difficult. The only enactment of caning on the hand I’m familiar with is a video clip from the ‘Grange Hill’ TV series showing a girl called Cathy Hargreaves being caned,