When you write a customized away message to a user in ICQ, (By Right click on a user -> Alert / Accept modes -> General -> Message -> Customize Message), only this specific user see what you write in the box there as your away message. The bad thing about it that the user can see that this is personalized message, by "Personal Message:" prefix before your personalized message. That's what we want to disable. Exit ICQ, Start your favorite resource editor (I recommend Resource Hacker from Here - Fast, easy & free), Load ICQ.exe from your ICQ directory, and then go to "String Table -> 688", when you open 688 you'll see there a number (Sometimes 1033, Sometimes 1038 and maybe other), click that number, and then look at the right side of the screen, There is a line:
11001, "Personal Message: "
Remove that line.
If you're using Resource Hacker, click Compile Script and then click File -> Save.
Close the resource editor, open up ICQ and then nobody can see that your away message is a personalized one.