A CrossFit WOD is exactly what you do NOT want to do on your rest days--that's the furthest thing from rest you can find. What you're looking to do is squeeze in some activity that allows you to move without taxing you at all. The reason things like working boxing technique and sled pulling fit this bill so well is that any kind of loaded eccentric movements are absent--they're also meant to be pretty low-level in terms of work.
Mountain biking may be all right if it's relatively brief and easy, but don't overdo it. Same goes for grappling--work technique at 50-60% effort instead of sparring at higher intensities.
Ultimately, you'll have to experiment to some degree to see what you can and can't tolerate. You may be able to get away with more than someone else, but most people need to keep their rest days super low intensity. I would suggest starting very easy and trying to gradually increase activity as you see fit. Otherwise you may end up spinning your wheels.