My approach, modify the following file.
includes/templates/YOUR_TEMPLATE/common/tpl_header.php

Please note below is my code for IE also.
HTML Code:
<!-->
<link href="/includes/templates/future_zen_4/css/ie.css" media="screen" rel="stylesheet" title="IE Style" type="text/css" />
<!-->
Put it, in the end of the below code section, and before the:
<!--bof-header logo and navigation display-->

PHP Code:
<?php
/**
 * Common Template - tpl_header.php
 *
 * this file can be copied to /templates/your_template_dir/pagename<br />
 * example: to override the privacy page<br />
 * make a directory /templates/my_template/privacy<br />
 * copy /templates/templates_defaults/common/tpl_footer.php to /templates/my_template/privacy/tpl_header.php<br />
 * to override the global settings and turn off the footer un-comment the following line:<br />
 * <br />
 * $flag_disable_header = true;<br />
 *
 * @package templateSystem
 * @copyright Copyright 2003-2006 Zen Cart Development Team
 * @copyright Portions Copyright 2003 osCommerce
 * @license http://www.zen-cart.com/license/2_0.txt GNU Public License V2.0
 * @version $Id: tpl_header.php 4066 2006-08-06 05:50:06Z ajeh $
*/
?>

<?php
  
// Display all header alerts via messageStack:
  
if ($messageStack->size('header') > 0) {
    echo 
$messageStack->output('header');
  }
  if (isset(
$_GET['error_message']) && zen_not_null($_GET['error_message'])) {
  echo 
htmlspecialchars(urldecode($_GET['error_message']));
  }
  if (isset(
$_GET['info_message']) && zen_not_null($_GET['info_message'])) {
   echo 
htmlspecialchars($_GET['info_message']);
} else {

}
?>
<!-->
<link href="/includes/templates/future_zen_4/css/ie.css" media="screen" rel="stylesheet" title="IE Style" type="text/css" />
<!-->
<!--bof-header logo and navigation display-->