Hello,
you can prevent from seeing your own idle time, by putting in the following into your remotes:
raw 317:*: halt
Note that this only prevents you from seeing your idle time, it won't prevent others from seeing it.
However, since you say that if you do a whois on other people, and you don't see their idle time, that either means they aren't idle, or that the network/server hides it.
In the latter case your problem is already solved, as you are the only one that can see your idle time, others can't.
Best way is to do a whois on yourself with a clone of yours. That way you will see what others can see when they do a whois. If it turns out that the idle time isn't displayed, then your problem is solved

If it turns out that you DO see the idle time when performing the whois on you through a clone of yours, then someone else should assist you. Because I have never seen a feature to hide your whois from others, though I woudln't be surprised if some networks provide such a feature.
Greetz