you only need the Wii's MAC address if you have MAC address
filtering / access control enabled on your access point.
tbh, having MAC filtering enabled is a good security measure
and will help to keep your network secure when used in conjunction
with WPA-TKIP (or AES) encryption.
have a look in your access point settings to see if you have got
MAC filtering / access control enabled...if so, simply enter the Wii's
MAC address into the "allowed" list.....you might also need to ensure
that the MAC filter rule is set to "allow" listed MAC's to connect and not
to "deny" them.