Technically no payment is due until the bag is delayed 24 hours and many airlines stick to that -- even BA in F refused any payment for the first 48 hours when they lost my bag at LHR. CX can provide you with a RON kit (remain overnight) which you might find useful, think they also have minor items such as t-shirts. Or you can ask for a set of the very nice CX F pyjamas made by Shanghai Tang (and sold for big bucks in their boutique). Might do quite well with out of this baggage delay if you play your cards right (CX has been known to throw in an opup to F, though their isn't F on the AKL flight but you could go via SYD I suppose).