How to remove https:// from shortcode generated url

That would be: return parse_url( get_site_url(), PHP_URL_HOST ) );

Explanation:

get_site_url is the WP function that returns the full url (it is the function that site_url relies on). parse_url is a PHP function that splits the url into several components and returns one or more of them. In this case it returns the hostname, which you seem to be looking for.