You can define a function to remove the protocol and hook it to the attachment URL:
function wpse_79958_remove_protocol_from_attachment($url) {
$url = str_replace(array('http:', 'https:'), '', $url);
return $url;
}
add_filter( 'attachment_link', 'wpse_79958_remove_protocol_from_attachment' );
Also consider to use relative URLs for attachments by using WordPress builtin function wp_make_link_relative
:
add_filter( 'attachment_link', 'wp_make_link_relative' );
Place this code to your functions.php
. Not tested though.
Update: already tested