At your own risk, you can watch the sketch for yourself at
https://www.youtube.com/watch?v=q9XJeL2MNpw.
In it, they say Hitler "just could not match" the humour, demonstrated by him telling the dog's nose joke (in English subtitles). The "German" words to the funniest joke, used to lethal effect by the British are, as described above, nonsensical gibberish.
The Wikipedia entry for this joke also confirms that it is nonsense.
https://en.wikipedia.org/wiki/The_Funniest_Joke_in_the_World
In the sketch, the Nazi attempt at their own V-joke weapon was the old chestnut: "There were zwie peanuts walking down the strasse, and one was assaulted (a salted) peanut."
If you try to input the "German" into Google Translate to get a version of it, it yields only links to this joke.
[Edited to update Google Translate Results and use correct links on August 21, 2016 by shuehorn]