Looks like the Quicktags API only accepts buttons, but we can trick the system with some jQuery as it does all sort of things ;)

The shortcode dropdown is built from var data and its behavior should be ajusted onchange:
add_action( 'admin_print_footer_scripts', 'quicktags_so_42200158' );
function quicktags_so_42200158() {
if ( wp_script_is( 'quicktags' ) ) {
wp_enqueue_script('jquery');
?>
<script>
/* Button name and callback will be replaced */
QTags.addButton( 'dummy_button', 'Dummy button', function(){} );
jQuery(window).load( function() {
jQ = jQuery;
/* Build dropdown - http://stackoverflow.com/a/4814600 */
var data = {
'-': 'Select shortcode',
'video': 'Video',
'audio': 'Audio'
}
var s = jQ('<select />');
s.attr('id','my-shortcodes');
for(var val in data) {
jQ('<option />', {value: val, text: data[val]}).appendTo(s);
}
/* Change 'Dummy button' for dropdown */
jQ('#qt_content_dummy_button')[0].outerHTML = s[0].outerHTML;
/* What will be inserted on HTML editor */
jQ('#my-shortcodes').on('change', function(){
var sc = '[' + jQ(this).val() + ']';
QTags.insertContent(sc);
});
});
</script>
<?php
}
}
Reference: A Deeper Look Into the WordPress Text Editor