I dont think there is a way with YouTube. Since private videos require a login to youtube, users watching it from vyew would need to be authenticated through youtube.
I wonder if there is a way to post a video as unlisted, so no one could find it unless they knew the address.
As for other hosting, there is probably not a way to make it completely private, because of the same issue above. Although any video hosting place that does not publish your url to a search engine will be relatively safe because nobody would know the url.
Possible solution
There might be a way that we could have the video loaded through a proxy on our end that would authenitcate users before they could load the video, that way they would never know the original address. I’ll check with the team.