Nearer, My God, To Thee was not listed in the White Star Line songbook. However, under the category “Suites, Fantasias, etc.” the songbook did have the general line, “National Anthems, Hymns &c., of all Nations”. This is one of those subjects that is open to question – could Nearer, My God, To Thee have been one of the unlisted hymns for which the band had an arrangement? If so, which version of the hymn?
The pianist conceivably could have played the four part harmony, with the strings dividing up the soprano, alto, tenor and bass voices. To stretch our imaginations, it could even be remotely possible that the band members read from a single copy – if they had very good eyesight and stood close together.
In the very last moments, would it have been musically possible for the band to improvise by ear – discussing beforehand which key to play it in, discussing which tune they should play (the one Americans would recognize, or British, or a particular band member's choice just because it was his personal favourite?), then explaining it to the Catholic bandsmen who may not have known it? To the public it may seem a simple matter for musicians who normally play from arrangements* to adjust to playing by ear on the spot, but indeed it is not.
*Did Titanic's band play from memory?
What was listed in the White Star Line MUSIC songbook? Part I
Titanic's final number: Hartley Solo Theory