How to skip the WooCommerce cart and go direct to checkout
The WooCommerce Fast Cart plugin lets you display the cart, checkout, or both in an on-page popup. Most people enable both, so that customers can add products to the cart and then access the cart and checkout in the popup. However, you can bring customers to the checkout more quickly by enabling the direct checkout option.
Full tutorial: How to add direct checkout to WooCommerce.
How to enable direct checkout
You can enable direct checkout in the plugin setup wizard or on the settings page. Simply tick the 'Direct checkout' box, and this will disable the fast cart.
Disabling the main cart and checkout pages
Even if you enable direct checkout, there might still be several back doors for customers to access the main cart page. For example, you might have added a 'Cart' link to the navigation menu, or your theme might add its own cart icon. The cart page contains links to the checkout, so customers can access the checkout page too.
You can completely prevent customers from accessing the main cart and checkout pages by enabling the Replace pages options in the plugin settings. That way, if a customer clicks on a link to the cart or checkout elsewhere in your store, then the fast cart popup will open. There will be no way for them to access the cart or checkout page.