Nothing in NZBDM deaths, nor the Wilson Collection for the correct James Woollett. (He is unlikely to be the one who died in 1949 as there is a likely NZ birth.)
Sources
"England and Wales Birth Registration Index, 1837-2008," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2XHL-M4W : 1 October 2014), James Woollett, 1872; from "England & Wales Births, 1837-2006," database, findmypast (http://www.findmypast.com : 2012); citing Birth Registration, Maidstone, Kent, England, citing General Register Office, Southport, England.
"New Zealand, Archives New Zealand, Passenger Lists, 1839-1973," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FSTF-4MS : 8 July 2019), James Woollett, 12 Apr 1874; citing ship , Archives New Zealand, Wellington; FHL microfilm 004412018.
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DNA Connections
It may be possible to confirm family relationships with James by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with James: