The line really only need have made sense to ONE person. What I mean is, I don't believe we have any evidence (and therefore should not assume) that this lyric was widely and frequently sung.

The chanty itself does not appear to have been very common, though we can't say for sure. I feel sure, however, that our perception of how common it was is quite skewed by things that have gone on since the end of the sailing era, e.g. through influential publications, recordings, revival performances, school text books, etc.

"Drunken Sailor" is almost in a class of its own in terms of form. One could say that it is unlike 99.5% of chanties -- quite atypical. I think it was "outside" the world of the floating verses found in most other chanties, so unlikely that the lines floated over from them. It is a very old fashioned kind of chanty, and possibly obsolete or reserved for rare situations by the time mainstream modern chanties came into use.

In short, there is no reason to imagine that sailors were often running up and down decks shouting "Put him in bed with the captain's daughter."

I have seen "Drunken Sailor" referenced only twice in all of the 19th century.

The first is an account of an 1839/40 whaling voyage out of New London (CT) to the Pacific.

...But there are many songs in common use among seamen, of a very lively character, which though bereft of all sentiment and sense in many instances, are performed with very good effect when there is a long line of men hauling together. ...Sometimes they all sing together as I have endeavored to represent, although it must appear very tame without the attendant circumstances. One of the songs is as follows:—

Ho! Ho! and up she rises
Ho ! Ho ! and up she rises
Ho! Ho ! and up she rises,
Early in the morning.


Source: Olmsted, F.A. 1841. Incidents of a Whaling Voyage. New York: D. Appleton & Co.

The second is a mention in non-maritime literature. A story/anecdote is related containing a scene of a woman cook at a home who gets drunk, messes up the kitchen, and is found singing the following:

Hee roar, up she rouses,
What shall we do with the drunken sailor?

Source: Dickens, Charles ed. 1855. "Two Dinner Failures." Household Words No. 256 (15 September 1855): 164-168.

In 1906, after a slew of writers had been discussing chanties with nary a mention of the "walk-away" method, much less mention of Drunken Sailor, Masefield mentioned it.

Strictly speaking, there is a fourth variety of chanty, but it is a bastard variety, very seldom used. ...The bastard variety which I have just mentioned has no solo part. It is a runaway chorus, sung by all hands as they race along the deck with the rope. You hear it in tacking ship. It is a good song to sing when the main and mizzen yards are being swung simultaneously. All hands are at the braces straining taut, and at the order they burst into song and "run away with it," bringing the great yards round with a crash. It is a most cheery kind of chanty, and the excitement of the moment, and the sight of the great yards spinning round, and the noise of the stamping feet impress it on the mind. The favourite runaway chorus is:

"What shall we do with a drunken sailor? 

What shall we do with a drunken sailor? 

What shall we do with a drunken sailor, 
         
Early in the morning? 
      
Way, hay, there she rises, 
      
Way, hay, there she rises, 
      
Way, hay, there she rises, 
         
Early in the moming.
"Chuck him in the long-boat till he 
 gets sober,
Chuck him in the long-boat till he 
 gets sober,
Chuck him in the long-boat till he gets sober, 
         
Early in the morning. 
      
Way, hay, there she rises, 
      
Way, hay, there she rises, 
      
Way, hay, there she rises, 
         
Early in the morning.
It is sung to a vigorous tune in quick time. It is the custom among sailors to stamp with their feet at each "Way, hay." The effect is very spirited.

And later,

A RUNAWAY CHORUS
What shall we do with a drunken sailor? 

What shall we do with a drunken sailor? 

What shall we do with a drunken sailor? 
      
Early in the morning. 
   
Way, hay, there she rises, 
   
Way, hay, there she rises, 
   
Way, hay, there she rises, 
      
Early in the morning.

Chuck him in the long-boat till he gets sober, 


What shall we do with a drunken soldier? 


Lock him in the guardroom till he gets sober,


"Drunken Sailor" was certainly attested --after the fact-- by numerous individuals as a chanty that had been sung in 19th century. It turns up in Davis and Tozer's expanded edition (1906?), in Terry's collection (1921), in Bullen's (1914), in Harlow's (1962, in reference to 1870s), in Doerflinger (1951). At least one of the old timers recorded in the 1920s sang it. So it was certainly not rare, though somewhat mysterious why the 19th century writers ignored it.

The main idea, however, is that none of the sources I've mentioned cite the "captain's daughter" line. I think that comes first (?) in Colcord's 1924 collection. (I don't have it with me at the moment; perhaps someone could confirm.) So...whoever Colcord got it from was the "one" person who sang this line (Did any others, later, collect this line? Hugill has it, but he was culling verses from various sources, including Colcord.)

I guess what I am getting at is that rather than assume "captain's daughter" was a common usage of the 19th century that we need to discover, we can start with Colcord's informant. Where did he learn it. Did he make it up? What did he mean by it? Did Colcord mishear something? It may be more of a specific, incidental matter, rather than a general question of meanings.