Anyone related to the Secords of New Zealand is not descended from Laura Ingersoll Secord.
Laura was an Ingersoll and just married a Secord.
My gg grandfather Guy Stephen Secord was born in Niagara area, Canada in Sept 1833 and died in Rakaia, New Zealand in Aug 1868
He married Martha Dunford,(1842-1883) in Christchurch NZ on 2 June 1859 and they lived in Rakaia where he was a partner with Martha's Dad in a ferry and hotel.
Martha was the daughter of William Dunford and Elizabeth Smith and they all arrived at Lyttleton, from Wiltshire, England on the Cressy, 19 December, 1850
Guy is buried in Christchurch, NZ and Martha, William and Elizabeth are all buried in Rakaia, NZ
Their children were:
Alda Alice Adelaide Secord (1860-) Florence Amelia Theresa Secord (1862-1929) Maud Frances E Secord (1864-1866) Rose Henrietta Mary Secord (1865-1845) Charles William Edward Guy Secord (1867-1942) Lillian Harriet Georgina Secord (1868-)
The parents of Guy Stephen Secord were William Edwin Secord and Frances J Holden.
Williams parents were Stephen Secord and Hannah De Forest.
Stephens parents were James Secord and Madelaine Badeau.
Stephen had a younger brother named James who was born in New Rochelle, New York in 1773 and married Laura Ingersoll of Great Barrington, MA, in Canada.
Unless you have another line/branch can be found that married into the James Secord/Laura Ingersoll branch, then no, there is no direct connection beteen them and Guy Stephen secord.
I prefer our real direct line heroine anyway.
Check out Guy's gg grandmother, Sarah Kast McGinnis.