I custom parameters does not work that way. They are used to replace the placeholder tags in the shortcode content with the parameters you pass to the shortcode.
The text after : (colon) indicates the default value if no parameter is sent.
They cannot be used to fetch anything.
If I understood correctly on what you are trying to achieve, in your case you can create different shortcodes with different URLs as shortcode content and use the respective shortcode when you would need that URL in posts/pages.