To my knowledge, there is no way of disabling log on for just the local console in LDSD. Since you stated you do not want to uninstall the local console from the workstations, you could always delete or modify the console.exe.config on the workstations. If you delete the file or if modify it, they will reach the login screen but it will fail once they enter their credentials. If decide to modify it, just delete the entry between the " " in the two lines:
<add key="TPS Host" value="DELETE ME" />
<add key="Url" value="DELETE ME" />
This will prevent the console from connecting to the proper server. When they launch the application and try to log on, they will get:
Just dont change the consoles for the Administrators.