Dear Claywoman,
Twain penned more than one pornographic story. I think you will find "1601"
(not 1602) pornographic enough, but there is also "The Mammoth Cod" and
"Mark Twain on the Science of Onanism" which may fit this category according
to your definition. More Twain writings that fit into this category exist,
but these should prove to be what you are looking for.
Sincerely,
Twainman