As already noted, a fixed blade knife in Yosemite is not going to provide the same usefulness as a traditional campground. CWL touched on the most important point, you cannot harvest, gather, pick up or whatever else method of wood procurement you had in mind, do in Yosemite without risking getting in trouble. If you are bringing in firewood I would go ahead and bring in an ax as well.
With Yosemite having such a larger number of people everywhere but the back-country you will get many odd looks having a fixed blade knife strapped on. While I love Yosemite to death, it doesn't give me the feel of camping much with everything and everyone that is there, you are more likely to see strands of colored lights than a fixed blade knife. I would go ahead and play the tourist roll while walking around the valley, if you plan to get away and do some more obscure hikes then feel free to bring the knife along. If you plan to do the traditional thing such as; Half Dome, the various falls in the valley, Glacier Point to name a few I would just bring along a folder.
Either way, enjoy your trip.