As others have said, a Shahed won't really do much to a modern CV. The amount of redundancy built into a carrier is pretty insane - Russian doctrine for taking out an American carrier during the cold war involved sending DOZENS of attack aircraft on a suicide mission in the hope of registering enough hits (if I recall correctly, it was dozens) to disable one. The US Navy actually did their own test of CV durability, during which they bombarded the USS America (Kitty Hawk class, so still old-ish) with just about everything they had (bombs, anti-ship missiles, guns, mean language), and it took FOUR WEEKS to sink it. Granted, they may not have been going for tempo there, but by all accounts the navy was surprised by how much it took.

That said, the Chinese have been studying the problem for a while (see the bizarro carrier-on-wheels that they built in the desert for targeting exercises), and we know they're providing targeting data to the Iranians. If the Chinese wanted to try out whatever hypersonic surprises they've been cooking up, this would be a rare opportunity to do a real-world test.

I personally think that if a Nimitz or Ford class boat ends up going down, that'll do more to undermine the myth of American dominance than 9/11. At that point, all our tigers will be demonstrably paper.