Use a page as a template for a custom post type

If you are considering using a page with shortcodes, it sounds like you are really just creating a custom layout for the actual content of the post, not changing the full layout.

If so, you could just filter on ‘the_content’ and output your custom fields into that content. WordPress will default to use the standard single.php if no custom post type template is specified, but your fields will appear as part of the content section of the page.