You are using cart_shipping.list
it Allows you to retrieve the list of available shipping methods for a shopping cart (quote).
your Requirement is that you have to fetch all active shipping method available in that store.
Then you One Solution I have found that
Step 1: you can create your custom API to fetch the All active shipping method.
Step 2: To create a new API you can follow the steps which are giving my Magento it self link
Step 3: In your API method getActiveShippingMethods()
type below code.
public function getActiveShippingMethods()
{
$methods = array(array('value'=>'','label'=>Mage::helper('adminhtml')->__('--Please Select--')));
$activeCarriers = Mage::getSingleton('shipping/config')->getActiveCarriers();
foreach($activeCarriers as $carrierCode => $carrierModel)
{
$options = array();
if( $carrierMethods = $carrierModel->getAllowedMethods() )
{
foreach ($carrierMethods as $methodCode => $method)
{
$code= $carrierCode.'_'.$methodCode;
$options[]=array('value'=>$code,'label'=>$method);
}
$carrierTitle = Mage::getStoreConfig('carriers/'.$carrierCode.'/title');
}
$methods[]=array('value'=>$options,'label'=>$carrierTitle);
}
return $methods;
}
Step 4 : Refresh the cache and test the API.