Okay, hacked a bit around and finally got a small WordPress Plugin which WebP-enables your WordPress site.
You can choose to put the javscript in the header or footer of your WordPress site and you can choose if the script will allways be used or only if the browser of your visitor does not have native support for WebP. After activating the plugin you will find these settings on the “General Settings Page” of WordPress.
Remember this script only works for img-tags not for embed or object tags.
At the moment you can fetch the package here. I have requested a new svn repository at wordpress.org to put it there. This will take a few days.
So please use it, test it and let me hear your feedback. 🙂