Getting Shipment Increment ID by Order ID in Magento via SOAP

We have an integration with Magento built entirely around the SoapClient. For example, a shipment is created like so:

$this->_client = @new SoapClient($this->getWsdl(), $context);
        if ($this->_client) {
            $this->_session = $this->_client->login($this->magentoUser, $this->magentoKey);
            return $this;
        }

...

$result = $this->_client->salesOrderShipmentCreate(
            $this->_session,
            $id
        );
return $result;

And tracking is added similarly. The problem is, if I need to update tracking for whatever reason, I need the shipment_increment_id. From our system, I pull the order_id. So I need to query Magento to get the associated shipment_increment_id from the order_id.

So, this seems to be exactly the solution I need, however, there is no Mage object in our codebase, we're communicating entirely via the SoapClient. Looking through the docs on the sales object, I'm not really seeing a solution here.

How can I get the shipment ID using the order ID via Magento's SOAP API?

Using default methods of soap you wouldn't be able to get shipment id by order id. For this you need to override Mage/Sales/Model/Order/Shipment/Api.php and extend the method as mentioned below.

In app/code/local/Namespace/Modulename/etc/config.xml

<models>
    <sales>
        <rewrite>
            <order_shipment_api>Namespace_Modulename_Model_Sales_Order_Shipment_Api</order_shipment_api>
        </rewrite>
    </sales>
</models>

Now create a method in app/code/local/Namespace/Modulename/Model/Sales/Order/Shipment/Api.php

class Namespace_Modulename_Model_Sales_Order_Shipment_Api extends Mage_Sales_Model_Order_Shipment_Api
{
    /**
     * Retrieve shipment information
     *
     * @param string $shipmentIncrementId
     * @return array
     */
    public function info($id, $attribute = null)
    {
        if(!empty($attribute)){
            $ids = Mage::getModel('sales/order_shipment')->getCollection()
                ->addAttributeToFilter($attribute, $id)
                ->getAllIds();
            if (!empty($ids)) {
                reset($ids);
                $shipment = Mage::getModel('sales/order_shipment')->load(current($ids));
            }
        }else{
            $shipment = Mage::getModel('sales/order_shipment')->loadByIncrementId($id);
        }

        /* @var $shipment Mage_Sales_Model_Order_Shipment */
        if (!$shipment->getId()) {
            $this->_fault('not_exists');
        }

        $result = $this->_getAttributes($shipment, 'shipment');

        $result['items'] = array();
        foreach ($shipment->getAllItems() as $item) {
            $result['items'][] = $this->_getAttributes($item, 'shipment_item');
        }

        $result['tracks'] = array();
        foreach ($shipment->getAllTracks() as $track) {
            $result['tracks'][] = $this->_getAttributes($track, 'shipment_track');
        }

        $result['comments'] = array();
        foreach ($shipment->getCommentsCollection() as $comment) {
            $result['comments'][] = $this->_getAttributes($comment, 'shipment_comment');
        }

        return $result;
    }
}

Now you can call this Soap method to get shipment info (including shipment id)

$result = $this->_client->salesOrderShipmentInfo($sessionId, $orderId, 'order_id');
var_dump($result);