In my custom dimension I want to have a custom sky with the 6 sided texture for it, how would I do this?

You'd probably have to override the normal sky rendering; I'd recommend you take a look at the LevelRenderer class. To do that, you'll probably need mixins. I have no idea how to proceed from there, though, since I don't know much of anything about how to do this. I have a feeling that it won't be trivial, though.