You can use the privacy settings on YouTube and set your video to Unlisted. It should prevent your video from being found by anyone using the site normally.
If that's not good enough for you and you can build a custom widget, take a look at the use-assets sample. With this you can save the video file directly into your custom widget. And HTML5 has the Video tag, that allows videos to play directly in the browser with no need for an intermediate service or plug-in.
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City of Arlington, Texas