Calling Wordpress functions from a ShortCode generated Button

I have a need to create a button using a shortcode that when clicked, the button calls a server-side php script to process various WP functions as well as use the functions from one of my plugin's API.

I'm fine with creating a shortcode that creates a button.

Is this just a matter of writing my own PHP script? Or am I over thinking this?

My custom PHP script needs to do some processing - add some rows to a custom db table, and then redirect to a specified WP page. So the script needs to access WP functionality without creating any visual output .

Am I missing anything here?
Is it easy to include WP functionality into my PHP script?

Thanks for your help!