I'v spent quite a bit of time reading logs and manuscripts from 19th century naval vessels, as I used to work at a museum with a large collection of them. I'v never come across a reference to singing at work, I guess you just don't write down something that doesn't happen.

I have read volumes worth of pages describing work while the ships band or the duty fifer and drummer from the ships Marine detachment play marches, never a reference to singing. Fifeing and Drumming appear to have been unique to the young American Navy. The fife and drum when out of fashion in Europe during the early to mid 18h century, to be replaced by military bands.

As far as "ships fiddler" the only references I'v found of a duty fiddler on Royal Navy vessels is a medical officer, who's job it was to play dance tunes once a day to prevent diseases like scurvy. I have found 2 references to a "capstan fiddler" in the french navy, one from the 1760s the other 1770s. All mention of duty fiddlers I'v encountered are from the middle of the 18th century, no one was singing chantys then.

Though I do believe music during work may have been more common on Naval vessels than some believe. All of the significant collectors of Chantys agree that chantying developed during the Eearly to mid 1800s as a result of advancing technology making ships bigger, while financial interests caused the crews to grow proportionally smaller. This didn't happen in the navy, you just wouldn't have a 150 foot ship with 20-30 guys doing the work, you'd have hundreds of sailors, there's no need for the chanty.

As to the reference of men singing at the pumps. That makes perfect sense.