On the face of it, Alfred died about 60 years before he was born

I assume you mean born 1887, went to NZ 1923, died after 1925, as there were few settlers in NZ until after about 1840.
Go to
www.scotlandspeople.gov.uk, register and invest in 30 credits at a cost rather less than the cost of ordering one NZ birth, marriage or death certificate.
Use one of the credits to search for the marriage of Alfred Wells to Catherine Duncan, and 5 more to download a digital image of the marriage certificate. This will tell you the full names of both Alfred's and Catherine's parents, including their mothers' maiden names.
Use another credit to find Catherine's death certificate. She will be indexed under both her married and her maiden surname so she will be easy to find. Then use another 5 to download the image of that certificate too.
You now know the full names of both sets of parents. Use another 12 credits to find (assuming that they were married in Scotland) and download the images of the marriage certificates of both sets of parents, and you will have their ages (and therefore approximate dates of birth) and the full names of all the grandparents of both Alfred and Catherine.
And you'll still have enough credits left to look up one more document, for example an earlier marriage (if the couple married aft 1 January 1855), or the death of Catherine's mother.
I see from the New Zealand death indexes (at
https://bdmhistoricalrecords.dia.govt.nz/Home/ ) that Alfred Wells, aged 38, died in New Zealand in 1925. Have you got his death certificate?