Without some indication of dates, even to the nearest decade it is very difficult to give any positive answer. Jean Christie lived from 1903 to 1987. Her grandmother was Helen Carr Smith who had three brothers, James, Alexander and William. all born between 1850 and 1860. The name Christie did not come into the family until 1900 when Helen's daughter Helen Smith Anderson married Robert Christie so if Harry Christie Smith wa a nephew or grand nephew he would have been born after 1900.
The best line of enquiry would be to locate the death record of the daughter who died in childbirth. If this happened n Scotland it will be found on the scotlandspeople website. This will identify the parents and from that the marriage record can then be found. Scottish marriage records give the names of the parents of both parties.
The loss of the birth certificate in the fire in California is not of significance unless it was in the San Francisco fires of 1906 which would help to establish a decade but the physical piece of paper which we call the birth certificate is only an extract from a Registry of Births. Scotlandspeople have what is termed a Marine Register. This is a register of births on British merchant vessels where at least one of the parents was normally resident in Scotland.
All these records are accessible online on the scotlandspeople website at moderate cost. Images of the registers before 1913 can be downloaded, those after 1913 can be ordered at extra cost. Alternatively there are plenty of genealogists in Scotland who would be able to carry out research of the actual records in either Aberdeen or Edinburgh.
Hope this gives some pointers and you manage to locate your family but could I suggest that you think about likely dates in further queries.
regards George