I guess my only chance of finding out who Hume's parent were is to find a record of his birth at the church.
Not unless he was baptised in a minority denomination. Generally speaking going to the church is a waste of effort. All the pre-1855 baptism records of the Church of Scotland were collected in 1855, and are held in the General Register Office for Scotland. The contents of all these Old Parish Registers are indexed on Scotland's People
www.scotlandspeople.gov.uk where you can also view a digital image of the original document.
I will check the LDS and see if they have a film on pre 1855 records for Livingston as that is where Hume was supposed to have been born.
The records referred to above are the ones the LDS filmed, so if you can't find it on SP you almost certainly won't find it via the LDS.
It is possible that there might be a record in the Roman Catholic registers, which are also available through SP. If it was the Scottish Episcopal Church, any surviving registers will still be with the church or the diocese, but don't hold your breath. The records of many other minor denominations (Free Church etc) are in the National
Archives Records of Scotland but don't get your hopes too high - the Free Church only came into existence in 1843. I have checked the online catalogue and they do not hold any such registers for Livingston earlier than 1844. There are earlier ones for Bathgate and Linlithgow - Have a look for yourself - they are all catalogued under CH3/
I presume that Isabella Smith, aged 60, and Patrick Smith, aged 30, living at Blackburn, Livingston, in 1841 are Hume's widow and son? That it is he who, as Peter* Smith, married Mary Mackie and had a daughter Agnes in Shotts in 1846 and a son Hume in Livingston in 1849? And that George Smith, born Blackburn, living in Shotts in 1841 and 1851 with wife Mary Marshall and son Hume, born 1840, is another of Hume and Isabella's sons?
*The names Peter and Patrick are interchangeable in Scotland. If you mislay a Peter, try looking for Patrick, and vice versa.