Richard Dyer-Bennet sort of cleared the air with his "Mark Twain's 1601" recording, available again from Smithsonian Folkways. In addition to the bawdy recitation of "1601" there are these bawdy songs:

Old Joe Clark
The Old She-Crab
The Tailor's Boy
The Eer-i-e Canal
There was a Friar in Our Town
The Gathering of the Clan

Now not all the bawdy verses of "The Gathering of the Clan" were recorded. That would have filled up several CD's.

However, at least one reviewer was quite flabbergasted that Dyer-Bennet would recite and sing such vile stuff!

Cheerily,
Charley Noble