At this time WooCommerce is not supported by any static site generator or serverless hosting provider including Shifter.
While we wish and would love to add WooCommerce support, the complex nature of WooCommerce as an ecommerce plugin is not designed to work as static.
The necessary functions that allow for WooCommerce to use payment gateways, search functionality, product listings and more are lost after the static version is created.
A few alternatives and simple ecommerce solutions for WordPress on Shifter is Square, Shopify, Foxycart and more.
If you have more questions about ecommerce on Shifter just ask!