You could set it to No on the Product Type setting for Product Free Shipping:
Product Free Shipping Image Status - Catalog
Show the Free Shipping image/text in the catalog?
then, using your templates and overrides you could change the code in:
/includes/templates/your_template_dir/templates/tpl_product_free_shipping_info_display.php
and change the code for:
Code:
<!--bof free ship icon -->
<?php if(zen_get_product_is_always_free_shipping($products_id_current) && $flag_show_product_info_free_shipping) { ?>
to be:
Code:
<!--bof free ship icon -->
<?php if(zen_get_product_is_always_free_shipping($products_id_current)) { ?>
Bookmarks