Would Nintendo care? You might think that a tech company would want to avoid the publicity associated with sending C&D letters to a man of the cloth but as the God Squad/Geek Squad brouhaha shows, you can't predict the corporate benevolence factor.
Bottom line. We know that gambling is not on your church's to-do list, but if we were a betting blog, we think your kids program will probably be able to get by using the terminology -- provided it's only for a few months, and it's a low profile event (not part of a national campaign). (Part of the God Squad issue was that the use has continued for years.) It wouldn't hurt to include a subtitle to your program that will serve as a sort of a disclaimer. For example, "WiiConnect: The crossroads between gaming and spirituality," or some statement that highlights that you are using the Wii in an informational, non commercial manner.