Scala.js - Inject contents of css file into an inline <style> tag

I am trying to build a web app (in Scala.js and ScalaReact) which is going to be added as a self-contained widget inside a larger web app, over which I have no control (cannot write things into the tag).

My app is going to contain a few pages with different CSS styles but also a collection of generic styles, which need to be loaded together with the widget.

My only option is to add inline tags dynamically but I can't find a way to read the contents of a CSS file and dump it in the tag at compilation time.

I've tried using ScalaCSS which can do the trick but its DSL is incomplete and doesn't meet my requirements even closely.

How can I trick Scala.js into generating tags with contents taken from local CSS files?