I would go buy this plugin:
http://adminmenueditor.com
Edit the menu to just include the add product function. Give your users some instruction on how to add products and away you go.
That paid plugin will not work at all period unless the WooCommerce settings are configured to allow people to access the admin area of WordPress – which overall is not a good idea.
Allowing people to add a product from the public side of the site can be done with any plugin that allows you to publish a form that, when submitted, can create a custom post type in WordPress. For WooCommerce, the post type name is “product” in all lowercase letters.
For example, you could do that Gravity Forms, which is not free. There might however be free plugins – not sure. You have to do some research.
