Before complete assembly of the hat I loosely coiled the LED strip around the had just to keep it neat but fully visible, and assembled the rest of the circuitry on a protoboard. It is easy to burn out these LEDs so as good practice I always put a 1000 uF capacitor across the power line and roughly 300 Ohm resistor in line with the digital control line.
The complete circuit diagram comes courtesy of Adafruit.
Here is the prototype circuit
Everything worked as expected. Before assembling the hat I ran a strandtest to make sure the LED strip I bought off Amazon actually worked.