Your current method of applying updates require user initiation and interaction. I haven't considered the pros and cons for this but perhaps using the Microsoft Windows's Update approach would make sense. The Admin could specify to automatically download updates and optionally automatically install the updates. If the install is done automatically, it should be a silent/invisible install with no user interaction.
If we take it 1 step further, it would be nice to specify in the program settings as an option to check a local network share for updates. This way the administrator can download the update only once and put it in a local share on the network.