I'm not a mental health care professional.... but my advice is to keep talking to her and show that you take her concern seriously. Don't blow her off with "I'm perfectly safe honey". I'm not sure there are accurate statistics to show if cycling is safer than the car IN YOUR AREA. Then there is the per rider or per mile, etc, etc, etc. Perhaps the way to view riding is that it *might* be riskier but your track record indicates that you are not a careless cyclist. And the long term health benefits may outweigh the risks. Can you promise her that you would stop commuting if you felt it became unsafe (for some definition of unsafe)?

You do have life insurance such that if something were to happen to you (cycling or otherwise) your wife would not be eating cat food on the street, right?