You could edit your footer template and add the following at the very top of the template:
Code:
<if condition="$show['quickchooser']">
<div>
<select name="styleid" onchange="switch_id(this, 'style')">
<optgroup label="$vbphrase[quick_style_chooser]">
$quickchooserbits
</optgroup>
</select>
</div>
</if>
This code won;t have any effect if you are using the mobile autodetect add-on or the different domain, different style addon as these addons *force* the style...