Here is the end result:
I used these supplies:
I started by removing the laces and covering the soles with duct tape to prevent them from getting painted/dyed. Next I stippled the black fabric paint in random spots with a paintbrush to act as the deep recesses of space. I let that dry overnight. Then I used spray bottles with some watered-down Rit dye to add the aquamarine blue, violet, and wine colors. That also dried overnight. Then I stippled silver acrylic paint over the black to make it more subtle. Finally I flicked white fabric paint randomly around to look like stars or planets.
They turned out great; I was satisfied with the end result.
Here is the rest of the costume (I meant to get a pick the included the shoes, but some craft beer got in the way of remembering to do so):