Using Videos in Membership - How do I keep the link private?

Site URL: https://www.thetoolsbook.com

Hello,

I am adding videos to a member area, but I don't want people to be able to click through and watch the videos on YT because then they could just share that video link with anyone but this is premium, paid content.

Is there any way to remove the YouTube icon in the bottom R of an embedded video? I have removed the controls, but it doesn't remove the logo and the ability to link out. 

Alternatively, is there another service that will accommodate this since SS doesn't allow direct upload of videos?

Thanks,

Jenn