At the moment, we can update applications on Windows IoT Core via following ways.
- Using Microsoft Store
- Using Device Update Center
- Using Azure IoT Device Management
- Using OMA-DM
More details please see this document. The first three ways in above list need internet.Using OMA-DM seems an option in your scenario, the OMA-DM interface is supported in Windows 10 IoT Core and any OMA-DM compliant management solution can be used to install and update applications. You may not need a connection to the internet to use license. In this way, you need to configure a OMA DM server.
In addition, you can also create a custom service for updating the application. You can serve the application package in your server, the devices can load the package's url. And then use PackageManager to update the app.
Here is a topic about how to update the app from USB drive. You can refer to the implement. The difference is packageLocation, in that scenario it is a removable storage, while in your scenario you need to use network share instead.