Hi,
As a temporary solution, you could publish back the plugin and replace the content of the file "plugins/hikashoppayment/authorize/\authorize_thankyou.php" by:
<!doctype html>
<html xml:lang="en-gb" lang="en-gb" >
<head>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<base href="http://mysite.com/index.php" />
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<meta name="keywords" content="..." />
<meta name="rights" content="..." />
<meta name="description" content="...." />
<meta name="generator" content="Joomla! - Open Source Content Management" />
<title>Shop</title>
<link href="http://mysite.com/index.php/shopping/checkout/notify/notif_payment-authorize/tmpl-component?lang=en" rel="canonical" />
<link href="/templates/gantry/favicon.ico" rel="shortcut icon" type="image/vnd.microsoft.icon" />
<link rel="stylesheet" href="/media/com_hikashop/css/frontend_default.css?t=1432765682" type="text/css" />
<link rel="stylesheet" href="/templates/gantry/css-compiled/bootstrap.css" type="text/css" />
<link rel="stylesheet" href="/templates/gantry/css-compiled/master-a31b55a8185ef76ab8f839ab5a9feaf3.css" type="text/css" />
<link rel="stylesheet" href="/templates/gantry/css-compiled/mediaqueries.css" type="text/css" />
<link rel="stylesheet" href="/templates/gantry/css/gantry-custom.css" type="text/css" />
<style type="text/css">
#rt-logo {background: url(/images/header/gpsc_logo.png) 50% 0 no-repeat !important;}
#rt-logo {width: 192px;height: 73px;}
</style>
<script src="/media/com_hikashop/js/hikashop.js?v=240" type="text/javascript"></script>
<script src="/media/system/js/mootools-core.js" type="text/javascript"></script>
<script src="/media/system/js/core.js" type="text/javascript"></script>
<script src="/media/jui/js/jquery.min.js" type="text/javascript"></script>
<script src="/media/jui/js/jquery-noconflict.js" type="text/javascript"></script>
<script src="/media/jui/js/jquery-migrate.min.js" type="text/javascript"></script>
<script src="/media/jui/js/bootstrap.min.js" type="text/javascript"></script>
<script src="/media/system/js/mootools-more.js" type="text/javascript"></script>
<script src="/libraries/gantry/js/gantry-totop.js" type="text/javascript"></script>
<script src="/libraries/gantry/js/browser-engines.js" type="text/javascript"></script>
<script type="text/javascript">
window.hikashop.ready(function(){window.location='<?php echo $this->payment_params->return_url; ?>'});
</script>
</head>
<body class="component-body">
<div class="component-content">
<div id="system-message-container">
</div>
<div class="hikashop_authorize_thankyou" id="hikashop_authorize_thankyou">
<span id="hikashop_authorize_thankyou_message" class="hikashop_authorize_thankyou_message">
<?php echo JText::_('THANK_YOU_FOR_PURCHASE');
if(!empty($this->payment_params->return_url)){
echo '<br/><a href="'.$this->payment_params->return_url.'">'.JText::_('GO_BACK_TO_SHOP').'</a>';
}?>
</div>
</div>
</body>
</html>
This way all the header will be present and correct, so the Javascript should owork properly and do the redirect.