Then the skin was not properly coded, if it is not showing the style chooser.
I would compare the footer templates in the styles, you should see the following code.
Code:
<vb:if condition="$show['quickchooser']">
<select name="styleid" onchange="switch_id(this, 'style')">
<optgroup label="{vb:rawphrase quick_style_chooser}"><option class="hidden"></option></optgroup>
<vb:if condition="$quickchooserbits1">
<vb:if condition="$quickchooserbits2">
<optgroup label=" {vb:rawphrase standard_styles}">
</vb:if>
{vb:raw quickchooserbits1}
<vb:if condition="$quickchooserbits2">
</optgroup>
</vb:if>
</vb:if>
<vb:if condition="$quickchooserbits2">
<vb:if condition="$quickchooserbits1">
<optgroup label=" {vb:rawphrase mobile_styles}">
</vb:if>
{vb:raw quickchooserbits2}
<vb:if condition="$quickchooserbits1">
</optgroup>
</vb:if>
</vb:if>
</select>
</vb:if>
--------------- Added [DATE]1378498954[/DATE] at [TIME]1378498954[/TIME] ---------------
As a matter of fact, I wrote a tutorial on it,
https://vborg.vbsupport.ru/showthread.php?t=301925