Thank you! This was very helpful as we a restriction on using YouTube videos as well. I had to adapt this to use with V1 of ZenDesk. If there's a better way to do the following, let me know.

Head into the Settings -> Extensions

Make or edit a global CSS widget and added the following to the top:

@import url('//vjs.zencdn.net/4.2/video-js.css');

Make or edit a global JS widget and added the following:

var js = document.createElement("script");
js.setAttribute("type", "text/javascript");
js.setAttribute("src", "//vjs.zencdn.net/4.2/video.js");
document.getElementsByTagName("head")[0].appendChild(js);

Update the URL to get the version you want.

Thanks again!