Do I need to replace the control arm if the bushings are worn? What is the safety risk?

Likely the replacement control arm comes with new bushings, although I'm not an expert in that particular car.  Most come as a unified assembly these days, and for a car as widely produced as the Accord, you could probably replace the entire unit for cheaper than just replacing just the bushings, but I'm not an expert in that particular car. 

Its always worth it to replace bushings on control arms.  I wouldn't mess with anything that has to do with integrity of the front suspension, unless you live somewhere where the roads are perfect and pristine, you never have to make evasive maneuvers, and you don't ever turn.   It also can substantially effect the front end alignment, depending on how worn it actually is, which effects how straight the car goes on the highway, and how well it responds to steering input.

Front ends, while really sturdy, need to be intact to be operate as designed.   I realize you may not want to spend any money on it and want it to last another year, but its an  unfortunate false economy to not replace a control arm bushing.