Hi tidller
Not having much luck with this chap.
I see a William WOOLDRIDGE, labourer, aged 15 arriving into Sydney 1876 with his parents William, shoemaker, (native place: Isle of Wight) and Eliza (Surrey). This William appears to have been born in NSW but his parents and brothers(Essex) in UK. It does not look as though he fits.
I am assuming your man is the one at 19 Herbert St Portsea in 1881, apprentice shipwright, parents James and Caroline.
I wonder if he may have come as ship's crew.
Do you have any further information - could he have changed his name here in Australia?
Judith