Before you go into the union room to trade, they ask you to save and with the DS games you have to delete the old data before you can save a new game.
But what happens if you start a new game and go to trade and they ask you to save?
You would have to erase the old game.
In the curent games like BW and BW2 you can trade via wireless and infrared. You can switch the settings so you don't have to save on infrared. I'm not sure about the wireless.