Update: As of the December update, this probably doesn't work. Oh snap!

Download this file:

http://heranbago.com/wii/hosts.zip

Extract the file to this folder on Windows XP:

C:\WINDOWS\system32\drivers\etc

It might be a different folder based on your configuration. You also might want to back up the old file before you overwrite it, as using the modified hosts file will disable use of the shop channel!

Try running the shop channel on your Wii connecting to your computer through a WiFi dongle. It's been tested on my Nintendo Wi-Fi USB Connector and works. It should work with any connection that goes through your computer first like one of the many wireless AP devices that have been picking up for DS and PSP owners.

Unfortunatly, the browser in the shop channel lacks Flash support...

Enjoy!

To set it up manually on a Windows PC:

Go to "C:\WINDOWS\system32\drivers\etc\"
Open up the file "hosts" in notepad.

See this part?

127.0.0.1       localhost

Change it to:

127.0.0.1       localhost
72.41.109.2     oss.shop.wii.com

Make sure the "localhost" and "oss.shop.wii.com" line up!

To set it up manually on a Mac or Linux/Unix:

Enter "sudo nano /etc/hosts" in the Terminal. Perform the same edit as with the windows tweak.

Some distros might use "su; nano /etc/hosts" instead.

Thanks Quickman for reminding me about the hosts file and *nix clarification!
Thanks Zachary Hinchliffe for the Mac instructions!
Thanks mozy.org/wii for the WiiBrowse files I'm using!
Thanks WiiModWii for amazing DNS technical jargon!
Thanks GBAtemp for the front page! Woohoo!