If, a person knows what they doing, then one person can do this, but, docking the boat will not be easy.
I not sure what you consider a mini yacht to be, size wise. But, we have about a 70 foot boat with twin Diesel Engines. I works easiest to dock with one person driving and two people with ropes Bow and Stearn (That three total). Other than docking it easy for one person.

It depends on what you plan to do on your yacht, and what kind of yacht you are talking about. (Sail or motor)

If you are talking about sailing yacht, I’m sure you would need at least 2. However, if it is a motor yacht, i can tell you from experience of having a 56 foot motor yacht there is no problem operating it without help if you know what you are doing. I would never take it out alone just because its not worth the operating cost unless you have friends and family to be there with you, but you really don’t need a “crew” to help you sail the yacht providing you know everything about it. However, I have only done light harbor cruising, I’m not talking about going all around the Caribbean, that would just be very stupid because if it were you alone in a yacht in the Caribbean, i can’t imagine that would be very safe.

Oh yeah, and don’t call it a mini yacht in your story lol. You can describe its length to portray its size.

what is a mini yacht?? really there is no such thing as a mini yacht. A small yacht on the other hand starts out at 39 feet and above. Anything over 33 feet needs at least two people to handle a boat of that size. Whereas the bigger yachts require up to six people to handle the lines when docking.