In answer to your question, ” No, you don’t have to be registered. The type of ‘unofficial’ Yoga practice you mention exists, even in strictly regulated countries.”
One of the main reasons Yoga teachers go through a certification process and later another registration process, is to cover themselves from potential malpractice or negligence lawsuits.
A Yoga instructor may also pick up Yoga teacher liability insurance, for added protection.
This is a sad state of affairs when healers and Yoga teachers have to worry about being sued by their students and clients. Unfortunately, the temptation to sue a Yoga instructor, for their assets or possessions, exists in many countries and cultures.
However, in the case of teaching Yoga to close and honorable friends, you should be safe.