I am assuming you have more than one dispatcher instances and that you will want to invoke shell script on all those dispatcher instances. One of ways is to write a shell script on your author server. That shell script will in turn ssh into all the dispatcher instances and execute the script, you may maintain list of dispatcher instances in that shell script. From AEM author instance, you will be left with invoking a shell script on same server which is an easier task.
Reason i mentioned involving one more script in between your author and dispatcher server is that you will not have to rely on 3rd party libraries for doing remote script execution (using ssh).