Hi Graham,
I'm not sure about preventing the "hang-up" messages, but here is the way to remove the "time&date" stamp;
Usage Guidelines
Use the voicemail conversation subscriber msg-properties brief command in Cisco Unity Express configuration mode to specify that only a subset of the system-wide message properties (envelope) played on by voice mail for regular messages. By default, all of the standard message properties are played. When you use this command, the sender information, date, and time are stripped from the message properties playback.
There is an interaction with the setting of the voicemail conversation msg-properties day-of-week command because if brief message properties is enabled, the day-of-week setting has no impact.
Examples
The following example strips the sender information, date, and time from the message properties playback:
se-10-0-0-0# config t
se-10-0-0-0(config)# voicemail conversation subscriber msg-properties brief
http://www.cisco.com/en/US/docs/voice_ip_comm/unity_exp/rel3_2/Command/v_cmds_external_docbase_0900e4b1809ef89a_4container_external_docbase_0900e4b180c98eeb.html#wp1019294">http://www.cisco.com/en/US/docs/voice_ip_comm/unity_exp/rel3_2/Command/v_cmds_external_docbase_0900e4b1809ef89a_4container_external_docbase_0900e4b180c98eeb.html#wp1019294
Hope this helps!
Rob