Untested but you could try adding the following code to the parse_templates hook:
Code:
vB_Template::preRegister('header',array('quickchooserbits' => $quickchooserbits));
And then use the following in the vBulletin header template wherever you want it:
Code:
<form action="{vb:raw vboptions.forumhome}.php" method="get" id="style_select" class="footer_select">
<vb:if condition="$show['quickchooser']">
<select name="styleid" onchange="switch_id(this, 'style')">
<optgroup label="{vb:rawphrase quick_style_chooser}">
{vb:raw quickchooserbits}
</optgroup>
</select>
</vb:if>
</form>