(1) Uncheck General Settings > Appearance > "Always show root categories in the category list"
(2) Use...
Code:
<select onchange="window.location.href=this.value">
<option>{$lng.lbl_categories}...</option>
{foreach from=$categories_menu_list item=c name=categories}
<option value="home.php?cat={$c.categoryid}">{$c.category}</option>
{/foreach}
</select>
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(1) May affect your main category menu though... It looks like yours is a custom menu, so you might get away with it.