Autoplay video with sound mute button

I am testing a site at where we need the home page header to have a Vimeo (or similar) video as a full page header. We would like this to autoplay on the full screen version and to start with the sound on but to have a sound mute button as a visible control. No other video controls are required, we just want it to loop and allow the viewer to mute the sound. I can get it to do all this with the exception of the sound using Vimeo as a background video and am now looking at different video player options. Do you guys know how to do this?