Sharing Arduino pin 11 MISO and PWM
You want to use the same output pin for two devices, so you'd need to multiplex in the other direction (i.e. one input, two outputs).

The SD card already does that for you, it will completely ignore MOSI if its CS is unset -- that's the point of having a CS line.

So all that is left is having the other device ignore its PWM input and keep the previous state while you are addressing the SD card. Depending on the device, it may already have readymade logic for that, or it might not work at all because interrupting the PWM line will make it turn off.