What code should I use to display children of a custom post?

wp_list_pages calls get_pages internally and pass the argument list to get_pages so you can pass arguments whatever get_pages accept.

To display child posts on your single-{post_type}.php you need to call wp_list_pages with post_type parameter.

wp_list_pages will ignore post_type but it will pass this to get_pages.

Example:-

echo '<ul>';

wp_list_pages(array(
    'post_type' => 'show',
    'child_of' => get_the_ID(),
    'title_li' => false //Set to false to disable the heading
));

echo '</ul>';

The only benefit of using wp_list_pages is hierarchical display in case if you have grandchildren of a post. get_pages with foreach loop will always give you flat list regardless of child or grandchild.