I've always used vi for editing groups.
I assume that you are aware of the security risks of mucking around with suid root.
Check to see whats the group of /sbin/shutdown. In my case it's bin.
Edit the /etc/group file and append the user you want to execute the shutdown command to the line that begins with bin. Seperate them with commas.
Issue the command 'chmod 5754 shutdown' in the /sbin directory. This makes shutdown group executable and set uid root. When a member of the bin group executes the file it is actually executed as the root user (more or less).
There may be other ways to do this, and I'm sure someone else will share thier ideas.