“CC1”/“CC2” is only used to name pins (A5/B5) of a USB-C receptacle. For USB-C cable plug these pins are named “CC” (A5) and “VCONN” (B5).
For your use-case the “CC” pin of the plug needs a 5.1kΩ (±20%) pulldown to indicate that you’re a power sink, while “VCONN” must be left not-connected. This should suffice as long as you don’t draw more than 500 mA.
Your cable is what the USB-C specification calls a “Legacy Device Adapter”, i.e. same as any type-C to (standard/mini/micro) type-B cable except you don’t need any of the data lines and you replace the type-B plug by your custom plug. Here’s a diagram from the specification showing such a cable/adapter mated to a USB-C receptacle (on the left):
Pinout on USB-C plug:
GND: A1, B1, A12, B12, shell
VBUS: A4, B4, A9, B9
CC: A5
all other pins should be left not-connected.