You can integrate with Amazon with your Woocommerce site via WooCommerce extensions like Channel Unity. The extension would pass product and order data back and forth between Amazon and Woo. Our integration would continue to pass data back and forth between Woo and your POS.
I believe you can select what items you want to send to Amazon within Channel Unity or whichever extension you choose to use. Orders made on Amazon are sent and created in Woo, where our integrator picks them up and sends them to the POS.