You can remove the Wi-Fi board, but taking apart the iPod touch is not very much fun! It requires a lot of heat-gunning and small part prying.
Luckily, there is a really easy fix! A quick Google search told me that you can pretty easily block everything that uses Wi-Fi and require a password to access it.
Go to Settings>General>Restrictions>Enable Restrictions and it will ask for a 4 digit password. Then turn everything on.
This way, you can go back in and turn it off at a later time if you want to, and you don't have to worry about taking the device apart!
Hope this helps! Happy fixing!