Something like that maybe?
<form>
<input id="fileinput" type="file" style="display:none;"/>
</form>
<button id="falseinput">El Cucaratcha, for example</button>
<span id="selected_filename">No file selected</span>
<script>
$(document).ready( function() {
$('#falseinput').click(function(){
$("#fileinput").click();
});
});
$('#fileinput').change(function() {
$('#selected_filename').text($('#fileinput')[0].files[0].name);
});
</script>