We need a trick here...
Normal select-dropdown things won't accept styles. BUT. If there's a "size" parameter in the tag, almost any CSS will apply. With this in mind, I've created a fiddle that's practically equivalent to a normal select tag, plus the value can be edited manually like a ComboBox in visual languages (unless you put readonly in the input tag).
A simplified example:
...
A live example:
https://jsfiddle.net/7ac9us70/1052/
Note 1: Sorry for the gradients & all fancy stuff, no they're not necessary, yes I'm showing off, I know, hashtag onlyhuman, hashtag notproud.
Note 2: Those
tags don't encapsulate the options belonging under them as they normally should; this is intentional. It's better for the styling (the well-mannered way would be a lot less stylable), and yes this is painless and works in every browser.