One of the easiest ways would be to extend the shipping/info model with your own extension, add a method to load it from tracking number without the hash. You can also look at Mage_Shipping_Helper_Data::decodeTrackingHash() and see how to build the hash yourself.
I believe the intent behind the hash is to stop people from fishing for shipping info on orders/shippments that are not related to them.
If you have assigned this tracking number to the order then you should simply be able to loop through all the trackings attached to a order and call getNumber on each tracking object.
foreach ($order->getTracksCollection() as $_track){
$_track->getNumber();
}
This is how the default magento code does it in the order history tab in the admin section: app/code/core/Mage/Adminhtml/Block/Sales/Order/View/Tab/History.php
Best Answer
You can do it with below. Add below code in your app/code/local/Vendor/Module/etc/config.xml
Now create a file app\code\local\Vendor\Module\Block\Adminhtml\Sales\Order\Grid.php with below code.
Create file app/etc/modules/Vendor_Module.xml