How do I skip invoice generation altogether?

In order to skip invoice generation completely, simply add the following action to your themes  functions.php

function bewpi_skip_invoice_generation( $skip, $status, $order ) {
    // Do your stuff based on the order.

    return true; // True to skip.
add_filter( 'bewpi_skip_invoice_generation', 'bewpi_skip_invoice_generation', 10, 3 );

Please test the functionality on a development environment of your website. If it ceases to work, please revert back to the original state of your website and follow the tutorial again.