Sure, you would just use Radianz, and that is in fact what everyone does. This is a very solved problem! Bloomberg also operates a private network, and there are others too. These systems can operate perfectly well without access to the public Internet.
A couple of jobs ago I worked at a financial services firm with 2 networks and 2 PCs on everyone's desk. Rednet for outside connectivity, and an internal network for real work, and never the twain shall meet.
NO-ONE needs the Internet for real work, let's be honest, just for goofing off. Time we all started to prioritize security over mere convenience.