Dunno what to tell ya, but CCC seems to be required to run the newer drivers, when I close CCC via task manager (no option to disable/quit it that I am finding) I get a driver failure error. That is probably why you can't get more recent driver packages without CCC, they seem tightly integrated together. But you are stuck if they are not listing just the driver on the individual downloads page. It isn't that big of a package, 140MB... The bright side is, once installed, when it checks for updates, it will only download the parts that had been updated, meaning you won't have to download a full package.
EDIT: I am reading the release notes, you can install just the driver alone, but it is strongly suggested that you install both the latest driver and control center for stability reasons. The 12.1 driver was only released a few days ago, this is most likely why you can't find the driver by it self yet.
The AMD display driver and the AMD Catalyst™ Control Center / AMD Vision™ Engine Control Center can be downloaded independently of each other. However, for better stability and performance AMD recommends that both components be updated from the same AMD Catalyst™ release.