No, sorry. As with most consoles, the Wii contains DRM to prevent users installing their own software. Moral objections aside, this means it would be impossible to mod World of Goo on the Wii without some serious effort.

The author of GooTool does not own a Wii but is open to assisting any serious Wii hackers in their efforts. Particularly, the rewrite of GooTool 1.1 for the iPad has added the functionality to build a World to a remote device (over SSH in that case, but it could potentially be on a flash stick instead). However it seems unlikely that this facility will ever appear, and most certainly never on an un-modded Wii.