Fear is the mind-killer ... it is the little death which brings on the greater death.
If you are afraid, stay home. No need for you to be endangering others, out there panicking on your bike.
I am not totally kidding, either.
Or, more reasonably ... accept the fact that your odds of serious injury or death are a lot higher in your car, and probably higher in your bathroom. You cannot control cars in traffic, you cannot control meteors or wild animals, or criminals, or much else. What you can control is your mind. keep your mind on what it is, they tell me ... then just live. it's only life, after all.
No one can afford to get injured ... so don't.
If you really cannot handle riding on a bike path, for whatever reason ... don't. Everyone has limitations, attachments, odd notions ... if that is one of yours, go with it.
Sometimes trying to do what you are too afraid to do well creates a self-fulfilling prophecy situation.