I am a UNIX user but not an admin. I am asking our admins to create a "sudo" command to allow shutting down our AIX workstations gracefully (without just pulling the plug).
Is there a way to prevent the user from executing "shutdown" on another workstation or server on the network?

If they grant permissions to you only when you are trying to run a shutdown script, things are safe. They write the shutdown script, it checks what it is shutting down before it takes action.

They protect the script from change. sudo has fairly fine-grained controls on it. An admin could grant run only to certain users on the script. Mid-level management in one department for example.

Is this what you are asking?

Yes it could be by granting locally the use of shutdown command, I am sure it could also be done in smit/smitty... (using RBAC...)