Hi Crowboy,
Unfortunately there are no records in the Church Register Index for your Braithwaites.

I checked with a librarian and, while the records are extensive, they are not complete. There are no Babtist records for example.
But I did find a Henry Warton BRAITHWAITE, Railway Guard, who was a witness at the wedding in 1874 of Watson BRAITHWAITE and Agnes KEMP. Could he be the father of your lot?
In the 1881 electoral roll there is Henry Warton BRAITHWAITE of Blue Spur, Tuapeka electorate, miner.
I couldn't find any marriages for your four but there are several other Braithwaites with middle name Wharton marrying.
Sorry about that - you might have to splash out on a certificate after all!
Kind regards,
Stephanie