Oh, please don't! I like native controls. They actually work well. Every site I have ever seen that has reimplemented popups and scrollboxes and whatnot, has missed many of the little UI tweaks that help our experience and took three decades to get right in the first place. E.g.: if I veer briefly outside the width of a native popdown menu, it doesn't go away. At a lot of sites with some sort of popdown menu, if you go one pixel outside the boundaries, the menu goes away and you have to go up and re-select it. And if the site gets that bit right, there's other things they've missed. Reimplementing a GUI OS in Javascript is not a good use of our time....
I have completely agreed with this to date, which is why it has remained a select box. But the problem is you can't really style them effectively cross-browser and so now it sticks out like a sore thumb.