I was specifically addressing the OP’s “any other corporal punishment you can think of”, @JLeslie.
I didn’t receive a response to my question, “Is the question about spanking or tying to a chair?” I addressed ‘tying to a chair’ (which is similar to ‘strapping to a board’, which was legal in Missouri when I worked with juvenile offenders), omitted spanking, and moved on to “corporal punishment you can think of that happens in other countries where human rights are not respected at all.” All of which, I’m reasonably sure, would result in the quick and immediate arrest of a NYC teacher.
Even then, my original, unanswered question, “Public or private school?” probably still has merit.
I don’t know if private military schools can still allow caning or not.