By default WordPress doesn't support putting custom shortcodes in the widget area but there is a way to do it but you'll have to edit your themes functions.php file
This article explains it in detail : http://www.carriedils.com/extend-wordpress-widgets-without-plugin/
Once you are ready to begin you'll need to open up the functions.php file of your theme and paste in this code in at the bottom.
// Enable shortcodes in widgets
So what you need to do is :
- Create a draft post and insert the video as normal, maybe use the small skins
- That'll give you your shortcode, save your draft and then copy the shortcode
- Go into your Widgets area and see if there's one there for text/html
- If there is then paste your shortcode into that and save
- Then edit your functions.php file and insert that code and it should show
Once you do that your Video Skins will appear in your Sidebar Area.
*Only attempt this if you are experienced with editing WP Themes and make a back-up of your website before beginning.