Focal length of a lens doesn't change, regardless of what camera you mount it on. If you're using, say 16mm on a FX body, calculate hyperfocal distance for 16mm on FX.
I don't really use hyperfocal distance though. I'm not too concerned if things far away are out of focus (unless the object far away is the main subject). Stuff that are far away are supposed to be not as sharp, so you can have a sense of depth. That's how your eyes see things. So unless you specifically have something in the background as a subject of interest, I'd rather focus on your main subject and not be too concerned about getting everything absolutely sharp. I usually also try to make sure my foreground is sharp, because I personally find it distracting when something in the foreground is blur.