Mapping Analog Data to Shift Register

CrossRoads:
I think I would do this instead, if I understand the requirement:
Map the analog brightness to a PWM pin, use that to drive a transistor to control the LEDs.

Thanks for the response!!!
I've never worked with transistors before but I just read up a bit and watched this vid to try and understand (about 8:50 on is the most relevant part):

From this explanation, it seems like your suggestion would be the easiest solution but do you have any examples of multiplexing with transistors and pwm like you're describing?
Thanks again.