Safari Bookmarklet for <video> AirPlay options – Copy the `bookmarket.js` snippet and paste it as the address of a bookmark in Safari. Then, while playing any <video> you can click the bookmarklet and the <video> will bring up your AirPlay options.

bookmarket.js

javascript:if(window.WebKitPlaybackTargetAvailabilityEvent){var videos=document.getElementsByTagName("video");if(videos.length>0)for(var airplayable=videos[0],i=0;i<videos.length;i++)if(!(airplayable=videos[i]).paused){airplayable.webkitShowPlaybackTargetPicker();break}}

raw.js

if (window.WebKitPlaybackTargetAvailabilityEvent) {
  var videos = document.getElementsByTagName("video");
  if (videos.length > 0) {
    var airplayable = videos[0];
    for (var i = 0; i < videos.length; i++) {
      airplayable = videos[i];
      if (airplayable.paused) {
        continue;
      }
      airplayable.webkitShowPlaybackTargetPicker();
      break;
    }
  }
}