It doesn't work that way. Let me show you an example:
Bob has a gun from TF2 for use in TF2.
Bill has a sword from SK for use is SK.
They trade, and it is now like this:
Bob has a sword from SK for use in SK.
Bill has a gun from TF2 for use in TF2.
You can trade items from 2 different games, but they don't go over to items for another game. So Bob can only use his new sword in SK, and Bill can only use his new gun in TF2.
BTW, this belongs in General Discussion or New Recruits, but it's not to bad.