This is an example of how you can use the free Contact Form 7 plugin to create a WooCommerce product enquiry form. Display a button linking to your enquiry page in the product table, and create one or more enquiry pages for customers to click through to.
We've added the Woocommerce cart widget to the sidebar of this page.
Try adding some products from the quick order form and watch the cart updating in real-time. Customers can then click straight to the Checkout. This cuts out several steps of the usual WooCommerce order process and helps to increase your sales.