the wifi lib is buggy but still this isn't a question about that. ssid must be set to public broadcast for the nds to make the connection with your router. it says so in the tech documents on nintendo.com. you can always dial that 1800 number on the back of your nds and talk to a free tech support person. i've heard you can turn it off after you are playing, but really i don't see the point. your broadcast goes what - 30 feet? do you have shady 12yr old neighbors that like to crack wep keys or something?
its good to be paranoid, but i wouldn't worry to much about it.
-another world