To answer my own question, Papers Past have, on SHIPPING TELEGRAMS. Star , Issue 4612, 7 April 1893, Page 3, Tainui arrived from London via Teneriffe, Capetown, and Hobart, with passengers for Lyttelton. The saloon passengers included a Mr Starkey.
There are probably others in the timeframe. Have you tried the passenger indexes at the National Archives?

There was a footballer W. Starkey featuring in issues of the Bay Of Plenty Times around 1895.

Sue