In general, sshortcodes are not a programming construct, they are content macros. As content macros, their viability in being used outside of their content context is limited. Simplistic shortcodes, like the gallery/audio/video (and I am not sure even about them) might “render” without context, but advanced ones will need a properly set loop, and calls to wp_head and wp_footer.
There is no simple general way to use shortcodes in situations they were not designed to be used in, and each individual shortcode you might want to force into “working” might require a good understanding of its own code, and enviroment requirements, something that you might be able to achieve if you build a site, but is probably hopeless task if you are trying to creat some general theme or plugin.