OK. In Windows 10 I was able to totally stop it from updating. What I did:
In Control Panel-Windows Firewall I added 4 outgoing rules. New Rule -> Program -> This Program path and browsed to C:\Program Files (x86)\Universal Remote Control, Inc\Complete Control Program.
I blocked ccp.exe, URCFrame.exe, URCLiveUpdate.exe, and URCLiveUpdate8.dll. Note that to block URCLiveUpdate8.dll I had to browse to the folder and then enter URCLiveUpdate8.dll.

Now when it starts it doesn't succeed in connecting to the mothership and thus no update available prompt. Also, if you select Live Update from Help -> Live Update it will fail as it cannot connect to the server.