This was a common occurrence, though the THREAT was much more frequently used as a disciplinary tool in itself. I don’t see the point of the argument about relative frequency between boys and girls. It simply depended on how naughty you were, not what sex you were.
I think there were certain areas in the UK, especially in the 1950s/early 60s, where girls were BEATEN or STRAPPED almost as much as boys. But I don’t believe the slipper was there from the start of Sec Mods as a palliative girls were treated the same as boys and were duly caned, or they were not corporally punished at all.
A couple of the girls I knew in my 20s who’d been slippered at sec mods in the late 60’s/early 70s went to schools where boys were caned, and also many more boys caned than girls were slippered.
And, as their mums or aunts had also been to the same schools, I have fairly good anecdotal evidence that, 18 years earlier, both sexes got the cane, but girls a lot less.