Mystery Monday - Who's that man?

In one of the bundles of photographs at home we have this one of a young soldier, presumably from the First World War period:

My grandfather, Malcolm, had four brothers who served in the war, John, Alexander, Duncan, and Peter.  The family sadly lost three of these boys in the war and only Peter and my grandfather (the youngest) survived, along with their sister Mary.

We presume that this is one of the boys, but do not know which one - as far as we can gather the boys served as follows:

• Peter Cameron Macdonald served as a private in the Argyll and Sutherland Highlanders, spending the war mostly in the Balkans and France

• John Macdonald was a corporal in the Argyll and Sutherland Highlanders (A company, 2nd battalion) and previously in the 93rd Highlanders.  He died at Arras, 24 April 1917 aged 25

• Alexander Macdonald was a sergeant in the Argyll and Sutherland Highlanders and in the Black Watch (8th battalion) - he died 19 July 1918, aged 23.

• Duncan MacCrimmon Macdonald was a private in the Highland Light Infantry (1st/5th battalion) and died 24 August 1918, aged 21.

Now, the man in the above photograph seems to have at least one stripe on his arm, which makes me think that it should be John or Alexander as they are the ones who held a rank above private (as far as we know), but we just do not know which of them it could be.

There is another photograph that may hint at this definitely being one of my grandfather's brothers:

 

In this photo (of my grandfather) there is another photo above the fireplace of a man in uniform with a moustache - this man looks a bit like the one in the photo that I began this blog post with - I have tried to zoom in a bit, but can't really get close enough to tell:

Anyway, the 'working hypothesis' is that it is probably John or Alexander in the 'big picture' and that this might be the same person in the 'little picture' seen at the family home.  If there are any military experts out there who recognise the cap badge, or anything distinctive about the uniform then I would love to hear from you...until then, my photograph remains labelled as simply 'probably one of the Macdonald boys'.