The code of the add to cart popup is on the "notice" file of the "product" view of your front-end template, and you can edit it via "Hikashop->Display->Views".
That code is displaying the "proceed to checkout" button :
echo $this->cartClass->displayButton(JText::_('PROCEED_TO_CHECKOUT'),'to_checkout',$this->params,$url_checkout,'window.top.location=\''.$url_checkout.'\';return false;','id="hikashop_add_to_cart_checkout_button"'); ?>
The path is not hard coded or stored in HikaShop.
HikaShop uses the live_site parameter of the Joomla configuration. So if you changed the URL of your website but didn't update the live_site parameter of the Joomla configuration file, you might get that problem.
Another possibility is that you have a third party SEF system caching the SEFed URLs and thus you don't see the change after changing the website URL but it doesn't seem to be the case here.