Senior Constable Carl Pedersen, of Oamaru, said the school had "everything under control" by the time police arrived.
While he confirmed a knife was involved, the cut "could easily" have been caused by the handle of the weapon.
Investigations were continuing.
Snr Constable Pedersen said it was never a good idea to be armed with a weapon in a situation that could escalate.
"Taking a knife into any situation where there is going to be a confrontation is just escalating it. If you think you are at risk, you just walk away.
"It could have been worse, but in saying that ... it only takes one punch for someone to fall the wrong way and that can be a lot worse. I said to the young man, if you hadn't taken the knife, the boy might have punched you and he might have been the offender.
"I just think that if people are planning a confrontation like that, from either side, they need to take a step back and think of the stupidity and risk involved.
"While it might seem like it's going to be a little tussle, it might escalate."