Thank you for your help! You led me to precisely the right places.
Here's the solution I'm going with for the moment (my customer has declared that each of his products will belong to only one category). I will be storing your information about the multiple categories for later use, because I am sure other customers' inventories will not be so well-defined.
I added this to the product->show template. It adds a 'Continue Shopping' button using the cart's current CSS style.
$link = hikashop_completeLink( 'category&cid=' . $this->element->category_id );
echo $this->cart->displayButton( JText::_('Continue Shopping'), 'category', $this->params, $link );