Hi, ages since you did your original post. My great grandmother (according to her son's marriage records) was Catherine Mackenzie of Scoraig, with her parents being William and Annabella Mackenzie according to her marriage records. She was born around 1842 so is very likely to be your relative John Mackenzie's brother.
I was interested that you say that you have all John's siblings' birth records, because I haven't been able to find Catherine's. If you do have it I would welcome sight of it.
As you say they were all called Mackenzie! Catherine married another John Mackenzie, also from Scoraig. His mother's maiden name was Mackenzie.
