The Folktrax recording of Wright's "Tally-I-O" is badly damaged with both static and skips. It is very problematic. For example, the Carpenter site transcribes the first line as "...was a jolly old soul," but after repeated listenings I still can't hear any "j" sound.

Here's the best I can do. I believe that everything is close to accurate but for what's in brackets.

                Tally-I-O was a silly old soul,
                        Tally-I-O! Tally-I-O!
                Tally-I-O was a silly old soul,
                        Come tally-I-O, you know!        

                What should I do with me rum, Sally-O?
                        Tally-I-O! Tally-I-O!        
                What should I do with me rum, Sally-O?
                        And sing tally-I-O, you know!

                We'll tell [them we're sober, O Sally-O!]
                        Tally-I-O! Tally-I-O!        
                We'll tell [them we're sober, O Sally-O!]
                        And sing tally-I-O, you know!

                Tally-I-O was a [?drunken] old soul,
                        Tally-I-O! Tally-I-O!        
                Tally-I-O was a [?drunken] old soul,
                        And sing Tally-I-O, you know!

The tune seems to me to resemble Hugill's but is not identical. Of greater interest is that "Tally hi ho, you know" is the title of one of the "lost" shanties mentioned by Dana as having been sung aboard the brig "Pilgrim" in 1834. There is also a song by J. S. Jones, in print by 1842, that begins with some shanty-like lines:

                A Yankee ship and a Yankee crew,
                Tally hi ho, you know;
                O'er the bright blue waves like a sea-bird flew;
                Sing hey aloft and alow.

Otherwise it's very flowery and was often reprinted. Finally, there are several shore songs with the refrain "Tally-hi-o, the Grinder," going back in print to 1804.