Right you are, Donna! See this wonderful Allan Sherman Discography. (If you follow the links, you can find lyrics to most of his songs.)

The discography lists HELLO MUDDUH, HELLO FADDUH (NEW 1964 VERSION) in addition to the 1963 original HELLO MUDDUH, HELLO FADDUH (A LETTER FROM CAMP). The two songs were issued together as a single (Warner Brothers 5449, 1964). The album "Best of Allan Sherman" (Rhino RNLP/RNC 005, 1979 - reissued on cassette as R4 70005) also includes both versions. However, that site doesn't give lyrics of the 1964 version.

There is also a very short song called HELLO MUDDAH - NEVADA STYLE which appears on the album "Allan Sherman - Live!!! (Hoping You Are The Same)" which was recorded in Las Vegas:

Hello mudduh, hello fadduh.
Here I am with John Ascuaga.
I just work here, he's the boss here.
I'm already operating at a loss here.

All the dealers are nice chaps here,
But the dice are full of craps here.
They're got style here, they've got class here,
And if you're not careful you can lose your chips here.