RGB and shift register

I'm making a pov hand fan and have gotten great advice so far. I want a medium/high resolution pov effect but due to the hand fan folding can't use an addressable strip. My plan is to use as many rgb leds as will fit and realize I will need to use shift registers. So my question is how can I minimize the amount of wires and space taken up on the fan itself? I would prefer to only have the leds on the fan with a quick connector at the base to attach to an external module with the arduino and power. But with four wires per led I don't see how it's possible. A standard shift register seems to large to put onto the fan to cut down on wires? Are there integrated micro shift registers like those on an adressable strip?

There are teensy tiny shift registers. Look at the circuit board of a cell phone. The hard part is soldering it.

Look around at some of the wearable technology stuff. I know they have wires for the lilypad that you can sew into cloth. Maybe something like that could be sewn into the fabric of the fan and wouldn't be so bulky.