I've only been up the east side of Clouds Rest once many years ago, but I sure don't recall it being anything scary, or like a "knife edge" ridge at all. I was on top from the west side just a few years ago, and there is quite a bit of flat, open space on top.
I can see on the Google Satellite view that there is a zig-zag trail that drops off to the south, and then joins the trail coming up from the west, but I don't think you would really need or want to use it.
If you have the time, the Mt Dana climb from Tioga Pass is another good conditioning hike.
