On board Titanic there were two ensembles: a salon quintet of two violins (Hartley and Hume), cello (Woodward), bass (Clarke) and piano (probably Taylor), and, additionally, the trio playing exclusively in the reception room outside the A la carte Restaurant and Café Parisien: violin - Belgian Georges Krins -, cello - French Roger Bricoux -, and piano - probably Theodore Brailey. This is not verified, but most plausible, because both, Roger Bricoux and Theodore Brailey, had previously served on the Cunard liner Carpathia
, together with violinist Edgar Heap. Theodore Brailey must have been accustomed to his French-speaking colleague, so why should they have separated, particularly because French was also the native language of violinist Georges Krins. Ensemble members like to stick together, when they have grown accustomed to each other.
I'm an amateur musicologist doing some private research in turn-of-the-century "Palm Court" music and very interested in this aspect of Titanic's history. I am convinced that Percy Taylor, who was a pianist - and is in some sources called a cellist (additionally?) -, did only play the piano(s) aboard the Titanic and not a cello. A salon quintet consisting of two violins, two celli and a bass might be, to put it mildly, very, very unusual. Two "high" and three "low" strings, what a sound! If you had no piano, but a cello and a bass, the fifth instrument usually was a third violin or a viola, or sometimes a woodwind (flute, clarinet), but not a second cello. Many string players are also pianists, but even if Percy Taylor was both, a pianist and a cellist, he would have left his cello at home.
So the cellist having smiled at Kate probably was John Woodward. And why shouldn't the have introduced themselves to each other?