I think it looks like a Fluttering. The throat is rather pale, less hooded than Hutton’s. Hutton’s also often has a dark wedge under the wing (in the armpit area) and darker underwings. Also worn Fluttering is often more mousy brown, rather than dark brown.
The bird also looks like it could be in primary moult. The pic is a little blurry, but there seems like a gap in the primary feathers. Fluttering moults earlier - birds I saw off Picton in January were moulting inner primaries - this bird looks like mid primaries. Hutton’s apparently moults later and in the wintering grounds off Australia, so moult is a great ID feature.
Fluttering breeds in the Marlborough Sound and is quite common there, whereas Hudson’s is generally found offshore from Kaikoura (birds breed in the mountains inland near there). Although I understand both species have been reported off Picton on occasions, I understand that Fluttering should be much the commoner.