Vaccinate the feral dogs. They will make a queue waging the tail, come to you and eat the vaccine from your own hands in 5 seconds if you show half a sausage. Save lottamoney in healthcare later and human lives. End of the problem. Vote me.
Or if you are more ambitious, caught them, mark the vaccinated dogs with a tatto or a ear tag, and give the poochie the whole sausage before releasing it again at their home, so people can know what dog interactions are safer and what need more care. Thus you avoid losing money vaccinating two times the same dog.
"should kill all the dogs because rabies" is stupid. Ecology models predict that that would spread faster the rabies and would made people less safe in that sense. You want territorial animals remaining in their territory.