Yes, it is possible to use SkookumScript with any engine and even to co-exist with Lua as you are adding it in.
On past projects that started with Lua, I actually added some commands in SkookumScript to call arbitrary Lua commands to help with the transition.
The GitHub UE4 Plugin is the best place to start. It has all the headers and precompiled libraries that you would need for different platforms. You just wouldn't need the actual UE4 plugin - though its code would be useful as a guide to integrate into your engine.
You would still use the SkookumIDE and get all of its features too - REPL live script snippets, debugging, live code changes, etc.
Here is a related forum post that also mentions the C++ classes you will need to derive your own custom subclasses and overridden methods for your engine:
And here is an older related post: