I was on CC the first part of April, and walked alone about the island while my BF was off diving. You many get some attention from some of the local men, but they are, for the most part, relatively respectful.
I would, of course, be aware when walking about at night. But one should be aware of surrounding when walking about at night anywhere in the world. I think CC is a whole lot safer than Belize City or any of the bigger cities.However,don't get too worried or be too paranoid about it. Use common sense , like any woman should. Ask the locals, ask whomever is running the place you stay at, ask the friendly bartender where or what is safe or not safe.