oddmuse-curl is kensanata’s tool to use Emacs to edit oddmuse wikis. I think it works rather well for my needs. Alternatively, I can also use the org exporter to export org mode content and manually copy this into a wiki page via the web browser. CLI options also exist to update the wiki, but I don’t think I need that functionality.
Borrowing off the documentation of oddmuse-curl, I was able to set this up, with some additional settings.