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WooCommerce is a Wordpress plugin, so no, you can't run it without Wordpress. If your goal is to make the backoffice simple to your client, you can strip all the unnecessary menu items from the sidebar, so he only sees the WooCommerce options. Take a look at this reference
WooCommerce is used by a number of high-traffic websites such as Small Press Expo.[11] For the 3rd week of September 2015, Trends indicated that WooCommerce ran on 30%[12] of e-commerce sites and millions of active installs.WooCommerce is an open source e-commerce plugin for WordPress. It is designed for small to large-sized online merchants using WordPress