Hi,
I’m not clear on whether you do or do not want the shortcodes, but if you don’t want them, you can call strip_shortcodes() on the text. If you do want them executed, use do_shortcode() on it.
I hope that’s enough info… Also, please be aware that not all shortcodes will work in a popup. For example, some need to load their own JavaScripts, and they won’t realized it’s necessary if the shortcode is embedded in a popup.