To quote the OP "She's afraid of (1) screwing up, and (2) something happening to me."
OK, simple...how do we fix both fears:
1. Screwing up: I suspect that this fear is the easy one to fix. Make it OK to screw up. I've been sailing over 30 years and hardly a day goes by on the boat where I don't do something wrong. 99% of screw ups are not life threatening. Yea, you might break a piece of equipment or put a scratch in it. You might tear a sail. So what. I found that when I was afraid of screw ups my crew was afraid of screw ups. Lead by example. Screw up then fix it and don't get upset.
2. Something Happening to You: Go the extra mile. Harness, inflatable vest, whatever. Don't be a hero, be a wimp. Then, let her do every job she wants to do on the boat. Every one. Encourage her to do jobs she is not comfortable with, and when she fails, smile, laugh and have her try again while telling a tail about how you screwed that job up first time you tried it to. Because you did but maybe it was so long ago you forgot.
Leadership is not doing things yourself, it's getting other people motivated and trained to do those things effectively. I don't know you so please don't take this personally, but I know many leaders who fail by leaving no room for failure. The only failure is not trying. It's not brain surgery or rocket science, its just sailing and it isn't that hard or even important. Make it fun.
It's of course more delicate in a relationship than employee/employer setting; however, a team is a team. Many, many years ago my then future wife and I got through some interesting weather and difficulties on a boat together working as a team. Those experiences were significant to us, and had a big impact on our decision to spend our lives together.
I think it might be a good idea to legislate a pre-marital test where couples need to spend time together living on a sailboat. If they survive a few weeks and still like each other, we would issue marriage certificates. There would be a much lower divorce rate
Good luck and may both of you find adventure, fun and happiness.