To make it so it's visible but not searchable, choose "unlisted" (not "private").
Quote:Private videos
A private video can only be seen by you and the users you select. The video won't appear on your channel or search results and will be invisible to other users. You can manage the users you want to share a private video with.
Under the "Privacy Settings' drop-down menu, click Share.
Add names from your Contacts or the email addresses of the people with whom you’d like to share your video. They’ll need a Google account to view your video.
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Unlisted videos
Making a video unlisted means that anyone who has the link to the video can view it. Unlisted videos don't show to viewers in the Videos tab of your channel page. Unlisted videos don't show up in YouTube's search results unless someone adds your unlisted video to a public playlist.
To share an unlisted video: Share the link with the people who want to have access to it, and they’ll be able to see it.
Unlike private videos, the people you share the video with do not need a Google account to see the video. Anyone with the link can also re-share it in a number of ways, such as simply forwarding the link. If you don't want to allow others to re-share your video, make it private.
