Most media players have some ability to set shuffle. Often it’s not just an on/off. For example, Logitech Media Server supports shuffle by song / shuffle by album.
I took a look at adding this to Squeeze. Looks like it’ll be easy for someone that knows what they’re doing to add support for setting the shuffle. But that someone isn’t me. I got bogged down in trying to figure out the right way to define things.
async_media_previous_track and similar functions already make a call to Squeeze that’s similar to the one needed to set shuffle.