Why look to Mishlei when you can see from the Gemara that corporal punishment is mutar?
The Gemara accepts corporal punishment to the extent that a rabbi or father who accidentally kills his son/pupil through corporal punishment is not even sent to an ir miklat. (Makkos 8a, Rambam Rotzeach 5:2). However, this is true only when the person giving corporal punishment is doing so for the sake of educational or character improvement – it is not a license for physical abuse, and this line can often become blurry.
In modern times, our thoughts about corporal punishment as a whole have changed. Today, we must follow the judgment of batei din based on their assessment of the needs of society (Aruch HaShulchan, 424:17).
All credit goes to my husband for the above.