Turn off ability to leave message when temp greeting on

I have a request by some users to disable the ability to leave a voicemail message when they have their temporary greeting enabled. Is there any way to do this? They want the ability to set the temporary greeting to have it play to the caller then hang up before the caller can leave a voicemail. The users want to do this themselves and not have IT help them record a message each time to create an announcement.

Does anyone have any suggestions?