The sort of shaped charge you could put on a thousand dollar missile could probably pierce small holes in the hull of a ship (too small to fly anything through,

The sort of shaped charge you could put on a thousand dollar missile could probably pierce small holes in the hull of a ship (too small to fly anything through, that is fantasy. Shaped charges are bigger than the holes they make.) But even hundreds of holes like that that wouldn't sink a ship. Not least because the ship is filled with sailors trained in damage control, and that sort of damage wouldn't be particularly hard to patch up. Clearing the flight deck with antipersonnel warheads would probably work better, but I wouldn't count on that to keep a carrier out of action for very long. If you really want to sink a ship, either use proper anti-ship warheads or don't bother trying.