You didn't say if you were already certified or not? Is your wife comfortable in the water ?
The main thing here is not to force someone to learn to dive if they really don't want to, it could be very dangerous. If someone is comfortable in the water they can overcome problems that may arise without panicing. As far as the fear of sharks, that is somewhat commom for people that don't spend much time around or in the ocean, about the only way you might get her to change her mind is by going somewhere nice to snorkle, so she could see the beauty of the underwater world and see that nothing is going to bother her.
I've been diving all over the world and have never seen any overly aggressive fish, including sharks, and I've seen alot of them too.
The only time anything underwater is going to bother anyone is if you bother it first.
The only exceptions are usually spearfishermen and outfits that actually bait the sharks. Sometimes the sharks will get worked up during a feeding.
Anymore, most divers pay big bucks just to get to see sharks, as they are being killed off by the millions every year for their fins.
You might take a vacation to Grand Cayman and let her dive with the Stingrays. ? But back to the top, if she isn't comfortable don't force her. If you want to dive, then I'm sure she wouldn't sitting on the beach while your diving.
Good luck