Just whatever you do, do not use Google docs to share information that belongs to a wiki. That's is by far the most annoying option and 100 times worse than just having to deal with a fandom wiki.
I agree, it'll also make a mess out of your "shared tab" on your drive. Me opening a document from som random doesn't mean that I want it to bury the documents that has been actively shared with me, from my wife for instance.