The reason fox's dair is good on shield as a mixup is because it has a ridiculously longer amount of hitlag than the other aerials (reason why it's easy to shield DI). If you throw it in occasionally, it will mess up people's timing for shield grabs and other out of shield options and make them get hit. Uair does a similar thing, and probably even fair if you're awesome. Nair and bair are too similar in timing to really throw people off.
Also, I'm pretty sure it is always theoretically possible to shieldgrab fox if he is doing multiple aerial/shines. Even with nair, which is the best framewise, you're going to have at least 7 frames before or after you're aerial (depending on how delayed it is). However, there is literally only one frame for grabbing possible since most grabs are 7 frames. Seeing as the fox can change the timing by quite a lot more than one frame, it is impossible to 'time' the shieldgrab, making it almost never happen vs. good fox shield pressure. I'm not sure, but I think dair is slightly worse on frames than nair/bair, so that 1 frame window is a couple frames longer probably, making it a little easier. Shine out of shield or sheik's nair are other things, though. They come out on frame 3 (fox's shine oos) or 4 (falco's shine oos and sheik's nair oos) and can be timed much easier. Still, you can't just rely on a static timing and have to adjust the timing you choose depending on how delayed you think the fox will aerial/shine.
I think that's basically it in a nutshell.
Oh yeah, if people are good at shield DI I don't think dair is that good. You can just shield di out of range of the shine and then fox has much less follow up options. However, he could just space a nair after, which is almost as good, especially vs. falcon.
Edit: Also, Falco's best shield pressure is theoretically with fair. If you time it right, you can make one hit come out on the top of their shield and the other come out right before you land, and then rinse and repeat. I don't remember the frames, but I think it's nearly as good as fox pressure. It's really hard to do consistently, though.