This hack used to work in <= Firefox 29 to remove a arrow:
text-overflow: \'\'; text-indent: 0.01px; -moz-appearance: none; >
Put the select in another container which has overflow: hidden;, make the select wider than the container. If you want a border, add it to the container.
overflow: hidden;
An example is the select at the bottom of this page: https://mozillians.org/en-US/