So the Shaw MacDuff profile is an issue indeed.
There is strong belief in him, and it's clear that he existed. And was all helpful in battle and what not, and became the leader of a clan.
That clan being the Macintoshes -- the name means "son of the leader."
And so far so good.
The tradition is that he is the son of Duncan, and certainly that fits the time line.
Here is a nice précis of where the info came from:
There have been two views taken of the origin of the Clan Mackintosh. According to the one, supported by a MS. of date 1467, the family can be traced to the Dalriadic kings; according to the other, founded on the Kinrara MS., which was completed about the year 1679, they are descended from the ancient Earls of Fife. For reasons assigned, Mr. Mackintosh follows the latter document as his chief authority for the earlier period. It is a family history written in English by Lachlan Mackintosh of Kinrara, brother of the 18th chief, and afterwards abbreviated and translated into Latin. This Lachlan quotes from three older MSS. which are now no longer extant. One of these was the work of Ferquhard, 12th chief; another, that of Andrew Macphail, parson of Croy; and the third was written by George Munro of Davochgartie.
Briefly, the account in the Kinrara MS. is, that Shaw, second son of Duncan, 3rd Earl of Fife, came to the north with King Malcolm IV. in 1163, to suppress a rebellion of the men of Moray; and that as a reward for his services he was made keeper or constable of the royal castle of Inverness, and received possession of the lands of Petty and Breachley, with the forest of Stratheme (Strathdearn). The name Mackintosh is said to mean ‘son of the thane,’ and this Shaw Macduff was the first to bear it, because his father, though an earl, was commonly called Toshachy that is, ‘thane.'
This is from The Mackintoshes and Clan Chattan. By A. M. Mackintosh, pp. xxiv, 566. Printed for the author, 1903.
I found it at. http://www.electricscotland.com/history/articles/chattan.htm
So the tradition is based on a 17th C MS, BUT that MS cites three earlier MS, now lost.
I would leave him as the son of Duncan, and add in all the scholarly info about where this all comes from.
One more wrinkle-- a scholar writing in 1922 says that this story makes no sense because Duncan was not a toiseich but a mormaer, so if he was Duncan's son his name should have been Mac Mhoireir. I'm not seeing a lot of traction for this, but I add it for the sake of fullness.