I think you have two choices
1) create a custom skin/extend an existing one and leave they button out of the template
2) use the `render_page` hook to modify the HTML before its sent to the client with something like (for the elastic skin):
if ($args['template'] == 'message') {
$args['content'] = preg_replace('/<a href="#all-headers" class="headers-all" onclick="return UI.headers_dialog\(\)">(.+?)<\/a>/', '', $args['content']);
}
return $args;
The plugin approach would give you the option to choose which users the button appears for.