Hi,
Using a view override and some PHP code ; yes it's possible.
The idea is to get the previous and the next order ID of the user ; so it requires to perform two SQL queries in order to catch them (or to perform just one query and them filter the return data in PHP).
Then, thanks to the two "order_id" (or less, if you're seeing the last or the first order.. Or if the customer just have one single order) ; you can create the buttons with the links.
Performing the SQL query will be like
$db = JFactory::getDBO();
$query = 'SELECT order_id FROM ' . hikashop_table('order') . ' WHERE order_id < ' . (int)$this->element->order_id . ' AND order_user_id = ' . (int)$this->element->order_user_id . ' AND order_type = ' . $db->Quote('sale');
$db->setQuery($query, 0, 1);
$previous_order_id = (int)$db->loadResult();
Regards,