Have you tried something like this:
.styled-select select {
-moz-appearance:none; /* Firefox */
-webkit-appearance:none; /* Safari and Chrome */
appearance:none;
}
Haven’t tested, but should work.
EDIT: It looks like Firefox doesn’t support this feature up until version 35 (read more here)
There is a workaround here, take a look at jsfiddle
on that post.