my priority would be to end the threat as quickly as possible without endangering others.

Only/last resort? Of course!

But there are people who think head shots are the only way to kill an animal. There are also people who are incapable of thinking, and they shoot a suspect animal and then walk away, leaving the carcass to contaminate other animals, and failing to notify the authorities so they could be aware of the problem.

As to endangering others, if there is one rabid animal around (esp domestic), there have to be others. It doesn't come from spontaneous generation.