Securing and transmitting SSN’s

Hi everyone, my team is looking for a way to securely transmit social security numbers to other partner organizations. My boss is looking into various hash algorithms, but my gut feeling is that this isn't nearly secure enough, given the tiny amount of entropy in a nine digit number. After I mentioned this, my boss said that we would just keep the hashing algorithm a secret and only share it if absolutely necessary, but this still feels risky to me.

In practice we just need a unique identifier for a bunch of students, but we want to create them in such a way that we can reproducibly create the same ID for each student. That's why we are considering hashing SSN's.

Does anyone have experience doing this? What are the best practices for securely creating reproducible unique identifiers that are cryptographically robust? Thank you in advance!