You do not need the discs, just the CS6 trial version installer.
Get that here:
Then you would buy a serial number from Adobe to permantly activate the installed trial software to either the standard or extended version.
If you want four permanent licenses (not cloud), ask about volume licensing.
I think you are misunderstanding a few things about Creative Cloud
The software is installed on your computer and the data never goes on the cloud unless you specifically choose to put it there.
You mention four copies, but one photographer. Each license allows two simultanious activations of Photoshop. Other people would not need Photoshop to view the images of course.
Your Creative Cloud subscription will NOT stop working if you are unable to log on to the internet for some weeks, (or even months if you have a years subscription).
You can pay for a full year in one go.
Other things to consider:
As a medical department, you would probably want to use the measurment tools that come with the Extended version. That makes CS6 a lot more expensive, but is an integral part of CC
There are some important features being added to CC that I can see your department making good use of.
Creative Cloud has a Teams option, although don't forget you can have two installations for each licence so long as both are used by the same person (deskop and laptop for instance)
I live in Marlborough, and I used to hate the permenent license model because of Adobe's price gouging. It used to cost me around 50% more for Photoshop than people using the same program bought in America. I am paying about NZ$23 a month for a Full Creative Cloud subscription of >30 applications. That is almost exactly the same as in America. Note this is the discounted first year price because I am a previous user, and it goes up to US$50 a month after that first year.
If you are able to qualify for the Photoshop Photographers bundle deal, you will get Photoshop CC and Lightroom for US$10 per month. That is such a bargain.
So all in all, I would advise you to think again about a Creative Cloud subscription.
I am in NZ and would happy to talk to you, although I am not in any way working for Adobe, and would not be able to help regards account details.