I used 1000 grit sandpaper. It's a bit cumbersome at first to get through the paint layer but once you start seeing the plastic, it gets easier.
If I remember correctly, it took me about 1.5h to completely remove the paint and I ended up with a smoth plastic surface.
Vinyl wrapping sounds like a cool idea, I have never done that.
You probably will have to figure something out with the holes where the two top rubber feet are located.
If you succeed, please show some pictures :)

Sebastian