I would start by looking at the following;

http://www.ssbits.com/embedding-youtube-or-vimeo-inside-your-text-content-using-a-custom-textparser/

This would allow you to create a tag that could be used in the content area to call in your widget. Then you would probably also need to create a method on a Page class to manually create your widget as there will be no Widget area as such. See the following for details of how to do that... (the Rendering a $Widget Individually bit)

http://doc.silverstripe.org/doku.php?id=widgets&s=widgets

Never done this myself, but this is where I would start looking.... not the easiest, hopefully someone else will post an obviously easier way that I don't know about!

Cheers
Jason