WordPress Woocommerce : show recent products, in a randomized order

I would like to display X recent products, randomly sorted, using a Woocommerce shortcode or a PHP function.

This shortcode...

[recent_products per_page="16" columns="4" orderby="rand"]

...displays 16 random products from the entire catalog (not the 16 last products randomly sorted).

Even if my Woocommerce settings specify that the default sorting is random, using this shortcode...

[recent_products per_page="16" columns="4"]

...displays the last 16 products ordered by date.