You can't access a github wiki via the github web API, which PyGithub uses exclusivly. But you can point your GitPython at the git URL of the wiki. After that you can access files in this git repo as with any other repo.
Edited
As you pointed out, that you restrict yourself not to create a local clone of the git repository I recommend following:
Read the code in https://github.com/github/gollum/blob/master/lib/gollum/frontend/app.rb which defines maybe all of the external HTTP interface.
A nicely wrapper around it for Python doesn't exist. But when you do make one (partially) than I recommend using a REST client library like mentioned here: https://stackoverflow.com/questions/2176561/which-is-the-best-python-library-to-make-rest-request-like-put-get-delete-pos
If you now think, that your restriction could be changed:
The documentation provides a good tutorial covering everything one needs with a little git knowledge. It boils down to:
import git
repo = git.Repo.clone_from("git@github.com:user/project.wiki.git", "some-path")
repo.index.add(["your-new-file"])
repo.index.commit("your message to the world")
repo.remotes.origin.push()