Custom block that's always the first thing in a region?
Your "custom HTML wrapper" is only useful for the Javascript, so you are looking at this the wrong way: the HTML generated by Drupal should not contain it, and it should be the job of the Javascript to transform the markup of the region to fit its use.

You probably want something like this:

$('&lt;your selector&gt;').each(function() {
  // Wrap all the content of the region inside a wrapper.
  $(this).wrapInner('&lt;div class="my-custom-wrapper" /&gt;');

  // Create a link and insert it into the region.
  var link = $('&lt;p&gt;&lt;a href="link-to-activate-dropdown"&gt;' + Drupal.t('Click here') + '&lt;/a&gt;&lt;/p&gt;');
  link.prependTo($(this)).click(function() {
    // Your custom logic.
  });
}