In IE9, it is possible with purely a hack as advised by @Spudley. Since you've customized height and width of the div and select, you need to change div:before
css to match yours.
In case if it is IE10 then using below css3 it is possible
select::-ms-expand {
display: none;
}
However if you're interested in jQuery plugin, try Chosen.js
or you can create your own in js.