WooCommerce : Sorting dropdown on 'Product category' shortcode

Dear wonderful you ^^
I am using the WooCommerce ‘Product category’ shortcode at some place on my site and need to allow customers to sort products with the regular dropdown, as on standard Category page.
I know you can pass an ‘orderby’ arg to the shortcode, but that’s not what I need, since I want user control on the sorting.
Does anyone knows how I could do that ?
I tried a few tricks but am too new to WordPress right now.
Thank you guys (and girlz)