PWM drivers of Shift registers that are not open drain?
Well, you could add pull-up resistors. If you need a lot, they are available in a SIL package which will reduce your part count:



But here's even less parts, if you can use a PNP transistor to switch the LED:



And, you can still use a SIL resistor package for R1. Also, Q1 does not saturate, which may make your PWM control easier, if your PWM frequency is high!