There is a History book of the Matheson's. "Alexander" appears about a 100 times in it. "1833" appears only 3 times, but none of them concern a birth year.
If you have time, maybe you could go thru all the "Alexander"s and find one associated with Cape Breton. Here is a link to the book:
Also, is there a living male descendant? If so, then a YDNA test would prove useful. Many, but not all Matheson's are descended from the Roderick that you linked to, or his father Murchadh Buidhe, who was clan chief in Loch Alsh.
Finally, just glancing at some of the many Alexander Matheson's, I see that there was an Alexander Matheson born in 1806 who had a son born in NS named Murdoch in 1835. That sorta works out, since your Alexander could possibly be the oldest son of the 1806 Alexander. I see him on listed on the FamilyTree DNA site, but not on WikiTree.