A Custom Category

I am looking for a way to make a category that when clicked on, will show all of my categories except for one…

On my blog I post youtube videos and sometimes blog posts. Some of the users will only be interested in the videos so I would like to have a category on the left side that is “videos only”. And when they click on it, it would show all posts except the blog posts.

I know I could accomplish this by going back and adding a new video category to all of my video posts but I hope there is an easier way as I have quite a few posts now. It seems like there should be an easy way to do this, maybe I am missing something, A plugin perhaps.

Thanks!