The song by Metchosin is the one I remember singing through the war. It is accurate except I think the last part of the chorus goes ..........And when swinging into action he's the centre of attraction, he's the pride of Bonnie Scotland so they say

The word used was into -- never intae (which is Glaswegian)

and I think the last 2 lines go .............
His red toorie-oorie-oorie-oorie-oorie-ay
His red toorie-oorie-oorie-ay