I had to do this once with my mom. It was fairly easy. I started with a call to the insurance company, who instructed me what to do. Next I called Carnival and cancelled. Three to four weeks later I received a check in the full amount of her fare. Carnival separately refunded taxes and fees.
In your case, when you know you have to cancel, I would cancel the specialty dining and shore excursion first. That will get Carnival processing that refund. Then call the insurance company for further instructions.
Hope your wife's surgery goes well and you are able to cruise as planned.