I've never done it and I don't know the best way to do it, but if you can't think of another solution, I'm fairly sure this should do the trick:
Don't even use a real box. I would maybe create it, but place some div over it that, when it is clicked, shows a hidden div that looks like the contents of the select box, containing radio buttons that are styled like s. Those radio buttons should then by styled to look like your example.