I've been looking about the internet for more info about 3.3v, and found this about the nano...
Power can be supplied to the Nano via the USB cable; feeding 5V directly into the 5V pin, or 7~12 (20 max, not recommended) into the Vin pin. You can only draw 3.3V at up to 50 mA when the Nano is running on USB power, as the 3.3V is sourced from the FTDI USB>serial IC. And the digital I/O pins still allow a current draw up to 40 mA each.
Im pretty sure that 50 ma wont be near enough, but If I resister the 5v input from the USB to 3.3v that may work. That way, the shift registers are powered directly from the USB, instead of through the arduino.
Its still going to need 17 resistors, which is messier than i would like, but less messy than 50 resistors.