Don't let it do anything you wouldn't let a full size stud do.
It's your choice.
But if its skittish I wouldn't keep it a stud.
I just got my Shetland stud gelded.
We didn't give him anything to calm him.
He was dropped in the pasture ( legs are tied up tight so he could kick or even get up)
I sat on his neck, he was snipped and stood back up.
I don't like drugging them if I don't have to.