Hi nz, and welcome to rootschat.
The headwear of the soldier on the left is commonly known as a "Tam" which is shortened from Tam O'Shanter. The army term is "Cap. T.O.S". There are certain items to the Tam that would tell you what regiment the wearer belonged too with out seeing the badge. For instance the Toorie on top of the crown of the Tam is a woollen "ball" and would have been red, brown, black depending on the Regiment. The backing material behind and at the base of the hackle, where the regimental cap badge would have been would also indicate the regiment, as would the colour and form of the hackle which is worn behind and above the regimental cap badge. In this case I think that the hackle would be the only way that you will be able to confirm which regiment the soldier was in. As you already have Alexander Cushnie as a name do you also know of the regiment that you say he served in, as a cross reference with the regiment headwear might help to confirm the soldier in the photograph's regiment (does that make sense?)
old rowley