I have done several where I have categorised them as "unlisted": this mean that only the person uploading them, and anyone he/she sends the link to, can view them: this works best if you have a large group of people to send a video to.
If you have only one person to send it to, then you can list it as private: if that person then decides they are happy for public viewing you can go back in and edit the category.
However the default setting is "public", so you need to check that this s what you want before releasing it to the world in entirety.