How to Update Shipment Number using API

As per our business requirement, we need to update the Shipment Number once we receive the unified Shipment ID from Transportation Management System.

We observe that we are able to modify the Shipment Number using the Edit Shipment UI successfully. Whereas we are trying to do the same using REST API 'ShipmentUpdate’ and there is no way to specify the new Shipment Number. Attributes are available only for updating Carrier, ModeOfTransportCode, ServiceLevelCode, etc. 

Kindly suggest if there is a way to update the Shipment number using REST API or SOAP services.