Hello @rkwood,

If you want to completely remove the cart system then you have to activate the child theme.

Child theme reference :
https://codex.wordpress.org/Child_Themes

You can also create the child theme using the plugin. Below is the link to one of them.
https://wordpress.org/plugins/wp-child-theme-generator/

After creating the child theme in you child theme functions.php file paste below give code .

https://gist.github.com/anonymous/9a0ade4b5f5d4f58afc52edbc28a41d7

Also if want to remove the Shopping cart link at the header please let us know.

Hope this helps.

Best Regards!!

Hello @rkwood,

To remove the shopping cart link at the header go to Admin Panel > Appearance > Customize > Additional CSS and paste below given CSS.

#right-header #cart-section li.cart-price {
    display: none;
}

Hope this helps.

Best Regards!!

Hello @rkwood,

To change the text in the buttom paste below given code in your child themes functions.php file

add_filter( 'woocommerce_product_add_to_cart_text', 'woo_custom_cart_button_text' );    

function woo_custom_cart_button_text() {
       return __( 'Contact us to order', 'woocommerce' );
}

Create the child theme using the steps mentioned in earlier reply .

Hope this helps.

Best Regards!!