Hi,
It should be doable. To avoid editing any of the core filey, I recommend the custom code below. Try adding this custom code to the functions.php in your theme/child theme directory. Before editing, please make sure to have a full site back-up just in case!
add_filter('asp_shortcode_output', 'change_asp_shortcode_output', 10, 2);
function change_asp_shortcode_output($html, $id) {
return str_replace("class='orig'", "class='orig' data-hj-allow", $html);
}