Off the top of my head I can think of a couple ways:
- Pull in the rendering script using the JSLink property of some other object, for instance, a Content Type, or a Field that will always be shown. This would require either having Powershell access to be able to set the property on something that already exists in the site, or you would need to be defining the Content Type or Field in VisualStudio. JSLink is a new attribute you can use declaratively in Field & Content Type definitions.
- Add a script editor or content editor web part to the Document Set welcome page, and embed or link to the rendering code there. You do not have to use the JSLink property for CSR overrides, it just happens to be a really handy way to ensure that a JavaScript file always gets loaded with something you always want it loaded for.
Here's another great resource for learning about CSR, that also mentions the fact that you do not need to use the JSLink property to load the script.
http://www.codeproject.com/Articles/620110/SharePoint-Client-Side-Rendering-List-Views
All that being said, the question in my mind now is: does the Document Set Contents web part even use the Client Side Rendering framework to render itself?