I don't allow users to change styles (this can be set in vBulletin Options) but if you do allow users to change styles this might work for removing a particular style form the quick chooser:
Edit your 'options' template which should look like this:
Code:
<option value="$optionvalue" class="$optionclass" $optionselected>$optiontitle</option>
and change it to the following:
Code:
<if condition="($optionvalue!=x) && ($optiontitle!='yyyyyy')">
<option value="$optionvalue" class="$optionclass" $optionselected>$optiontitle</option>
</if>
where x is the styleid of your mobile style and yyyyyy is the name of your mobile style. The name is case sensative!
This should stop it being added to the drop down list.