If at any point it is necessary to do random searches, it should be done in the most discreet and non-humiliating way. And by no means should a principal do it alone. He should ask the student to please come to the office and not indicate why, and then ask another adult to come in as well.
He should say to the student clearly “I am not accusing you of anything but you know that the Yeshiva has a policy of random search and I am supposed to enforce it. Do you have anything on your person that you should not have or is against the rules of the yeshiva? Would you mind emptying your pockets into this plastic bag?”
After it is done, the Principal should say “Thank you for your cooperation”. In this manner as he does the random search of any student and then of a student that he suspects, the students can compare experiences and see they were the same and that all were treated fairly. In addition, there would be another adult present to realize whether or not the principal is picking on any particular student and if he is treating all equally. If done with seichel and not bullying it does not have to become an issue.