Thanks, pavane. Mentioned and linked to before at THIS THREAD, but here again. The link to the sheet music is Levy Collection: Two Little Sailor Boys. The composer's name is "Dolly Jardon" on the score page, which seems to be correct.

Title: Two Little Sailor Boys. Song.
Composer, Lyricist, Arranger: Words by Edward Madden. Music by Dolly Jordon.
Publication: New York: Jerome H. Remick & Co., 1906.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: Two little chaps with sailor caps, played at a game of war
First Line of Chorus: Don't forget when we were sailor boys
Engraver, Lithographer, Artist: De Takals
Advertisement: ads on inside front and on back covers for Jerome H. Remick & Co. stock
Subject: Children playing
Subject: Campaigns & battles
Subject: Naval warfare
Subject: Rescues
Subject: Friendship
Subject: Courage
Call No.: Box: 150 Item: 085

~Masato