I want to add a global text that shows up on all products (not edit the product and add manually), is there a way without altering product template?
If you want it exactly after short description this is better:
add_filter('woocommerce_short_description','myglobal_short_descr');
function myglobal_short_descr($sdescription)
{
$text="Global Text Goes Here";
return $sdescription.$text;
}
Add this to functions.php of your theme
add_action( 'woocommerce_before_single_product', 'add_text_after_excerpt_single_product', 25 );
function add_text_after_excerpt_single_product()
{ global $product;
// Output your custom text
echo 'Global Text Goes Here';
}