I haven't heard of that -- wearing them on certain sides. I'd suggest doing one of a couple of things: if you have two lanyards or a lanyard and something else for wearing pins (like a vest etc. I just got one of those hip lanyards off of ebay), put the ones you don't want to trade on a separate lanyard or the vest. Explain which is your trading lanyard.

Or just kindly explain that you can't trade certain ones. Be firm, friendly, and don't feel guilty!