I sympathise with your problem which was caused by CX rather than by you - but I would strongly recommend getting the tickets and pnr changed to the correct name - in my previous job as a travel agent I have found all US carriers to be more and more strict about correct names in bookings - to the extent that I can remember some instances where the airline actually cancelled reservations that only had initials .

I am very surprised at CX making a booking on an itinerary involving the US without a full name - my understanding is that all major carriers to / from the US have required full name/passport matching for quite some time.

In a situation where your wife's name cannot fit into the ticket field it does get quite tricky - some countries permit an endorsement in the passport stating "also known as" unfortunately with the current level of paranoia in the US this could also be asking for trouble.

If I were you I would go back to CX and press them to waive the reissue fee - but if they wont I would still get the tickets changed at my own expense - it is simply not worth the risk

good luck