Max, it's good to see that you read the Scriptures carefully. There probably isn't an absolute answer to your question, but the following seems very likely: Joseph had just come out of prison and was not looking or smelling his best. The change of clothes is rather obvious. He was appearing before the most powerful man in several lands and this was a very important meeting. He wasn't representing just himself, but also his God, Jehovah. Therefore he would want to present himiself well. By shaving, thus appearing more Egyptian, he could lessen any prejudices Pharaoh might have had. Centuries later Paul wrote that he became as a Jew to Jews and as a Greek to Greeks, all things to all men in order to save some. It appears that the principle has held true throughout the ages. Whether he shaved his head, beard or both, we can't be certain, though likely both as this was the Egyptian style. Since Joseph wasn't under the Law yet to be given to Moses, he wasn't trangressing by shaving. As to why it's mentioned, here are a few possibilities. It demonstrates that God's people may conform to local custom that doesn't violate His principles or commands. It also feeds the narrative, supporting the fact that his brothers didn't recognize him since he appeared as an Egyptian, along with the fact that time had passed since they had seen him. The Bible is a unified whole and as you continue to read and study, you will find that little tidbits that you pick up here and there will make other accounts and teachings make more sense. Keep on reading carefully as you have and you will find countless treasures that the casual reader misses.