Here is the track list from "Colonial & Revolutionary War Sea Songs & Chanteys" - that's the actual title - by Cliff Haslam & John Millar, taken from the notes to the vinyl edition (FH 5275).

Boston Harbour (c. 1765)
Sam's Gone Away (18th C.)
Johnny Todd (18th C.)
Pleasant & Delightful (1756)
My Son John (18th C.)
Polly on the Shore (18th C.)
Anti-Gallican Privateer (1781)
Fathom the Bowl(18th C.)
The Pressgang (18th C.)
All the Things Were Quite Silent (18th C.)
Here Comes Captain John Paul Jones (1779)
Fare Thee Well My Dearest Nancy (18th C.)
Adieu Sweet Lovely Nancy (18th C.)
Pretty Nancy of Yarmouth (18th C.)
Yankee Privateer (c. 1780)
An American Frigate (1779)
Stately American (1778)
Yankee Man of War (1778)
Sir Peter Parker (1776)

Of all these selections, only two - Boston Harbor and Sam's Gone Away - are identified as chanteys. The rest are , presumably forebitters or simply songs about the war and the sea.

For what it's worth, there's an address and telephone number of Seaport '76, the organization that had a hand in producing this recording. These are 25-year-old entries, so I would not be surprised if they are not still valid.
Seaport '76
60 Church Street
Newport, RI 02840
(401) 846-1776

Cliff Haslam is still active in performing here in Connecticut - mostly around Essex, near where he lives. I don't have contact info right at hand, but it shouldn't be too hard to dig up, if needed.

Regards,
John