Disable OS X Server's shutdown prompt?
One possible way could be by using a terminal command:

shutdown -h now


This immediately kills all processes and shuts your system down in a fairly nice manner.

As a normal user you could initiate this by 

sudo shutdown -h now


But the problem with password prompt remains, this time in the terminal.

Having a closer look to the sudo configuration file /etc/sudoers I found:

...
# User privilege specification
root    ALL=(ALL) ALL
%admin  ALL=(ALL) ALL

# Uncomment to allow people in group wheel to run all commands
# %wheel        ALL=(ALL) ALL

# Same thing without a password
# %wheel        ALL=(ALL) NOPASSWD: ALL
...


Check whether your account is already in the wheel or admin group by issueing groups in the terminal. If that is the case, just uncomment the line with %wheel NOPASSWD or by adding NOPASSWD at the proper position of the admin line above (the wheel line shows you how to do this). For instance:

tatooine-3:~ mallert$ groups
staff com.apple.sharepoint.group.2 everyone localaccounts _appserverusr
admin _appserveradm _lpadmin _appstore _lpoperator _developer
com.apple.access_screensharing com.apple.access_ssh com.apple.sharepoint.group.1


Here my user is already in the admin group, therefore I would just add NOPASSWD in the sudoers line like this:

%admin  ALL=(ALL) NOPASSWD ALL


Now you should be able to fire up a 

sudo shutdown -h now


without being asked for a password. To finalize my solution you could create an app with automator which executes this sudo shutdown -k now command as a bash script.

If you want to reboot the server instead, use

sudo shutdown -r now