I have tried, without success to find his date of birth
What sources have you tried?
If he was 23 in November 1944, he would have been born in 1921 or possibly late in 1920. So he could have been born before the 1921 census, which was taken on 19 June 1921.
Searching the 1921 census index for a William M*ck*n*z*, aged 0 to 1, with a Helen in the same household, produces one result, in Canongate, ED34 Page 10.
Plugging that into the search produces a listing for William McKenzie, 34; Helen G, 32; Annabella, 8; Jean, 5; William M, 0.
William Moffat McKenzie was born in Canongate on 26 January 1921, parents William McKenzie and Helen Gordon.
Annabella McKenzie, mother's surname Gordon, was born in South Leith in 1913.
There is no death in the index of a William Moffat McKenzie of the right age.
So I think William Moffat McKenzie is a good candidate to be the one you are looking for. Unless your one was born after 19 June 1921, or he was not born in Edinburgh.
