You're sounding like a Catholic apologist.
So if the oral things were not written, where can one find them?
The answer is in the Church, the leaders of which were told to go into the whole world and teach all things that were commanded them by Christ. Mt 28:20
Oral things handed down, like divine revelation were taught to Timothy, doctrinal instruction, authoritative teaching. The point being Paul does not mention anybody or anything that he should look to for help in teaching or mattesr of faith, the Holy Spirit was there for him, not some organization.
Tradition from fallible, corruptible men or God breathed Scripture, not a difficult choice.