The CCC doesn't effect fan speed. It controls the AC compressor though.
It's hard to say if reinstalling all the CCC stuff would be better for you at your point since you already spent the money on a non CCC carb/distributor amd ( presumably ) a converter lockup kit, but if you still have all of your CCC parts and it ran fine with them, that's the route I would go. You can always sell your other carb/dist.
My 350 was running on the CCC system. In fact it was built specifically to run perfect with it. The only reason I deleted it was because I was becoming frusterated with a minor tuning issue and I wanted to swap on an RPM intake manifold in my quest for more performance. In the end, my tuning issue and lack of expected performance was the fault of the $hit engine build from the crooks at Rocket Racing. If it weren't for that, my engine would still be running on the CCC system.