Nothing is risk-free. But your perception of risk is almost certainly distorted. Cycling is surprisingly safe. The fact that someone has been killed in ypur vicinity doesn't change that, all it changes is your level of anxiety. Other people have died in your vicinity while driving automobiles, or falling down stairs, but that hasn't had a similar impact on you because you don't feel yourself to be at significant risk when undertaking those activities.
So the way to address the problem is to manage your fear. You do that by practising your riding skills, as FBinNY suggested, and building your confidence in your own ability to ride safely. That will immediately put you well ahead of the game - a disproportionate number of the cyclists who do get hurt are either drunk, riding at night without lights, riding against traffic etc. Then start riding on relatively quiet street where the traffic isn't too intense, and get used to that. Then move on up. You'll find that it is surprisingly easy to become accustomed to and fairly comfortable with quite heavy traffic.