Hiding a blocks edit links

I am trying to hide a specific blocks edit links that appear on hover. Here is the function I'm using right now, the first commented line makes the items not hidden, but not anything more. The next line was an attempt at removing the include on line 563 of zen's template.php, but didn't result in any change.

function project_preprocess_block(&$vars, $hook) {
  if($key = array_search('block-menu-menu-user-links',$vars['classes_array'])) {
    //$vars['classes_array'][$key] = '';
    unset($vars['edit_links_array']);
  }
}

The problem is I have this menu in one line, and the hover links cover items.

And I've already cleared all the caches, so that can't be an issue.