The Scottish units in Swedish service are surrounded by a large number of myths and misunderstandings due to the errors made by 19th Century historians which have been kept alive due to overreliance on English language sources by many later day historians. A good example is MackKays regiment which was never called a highland regiment in period sources nor was it made up of highlanders, in fact more than a few of the men were not Scots at all.
A look at the muster rolls for Lt-Col Monro's Squadron of MacKay's regiment show that Robert Monro's own company was made up of Scots (72%), Englishmen (8%), Germans (11%) and Danes (9%). Robert Monro of Foulis company was rougly 50% Scots and 50% Germans & Danes. John Monro's company had roughly 2/3 Scots, Sinnot's company was 19% Scots and 81% Germans, Learmonth's company was mostly Scots with some _Irish and English as well while Bullion's company was entirely German.
The 2nd squadron of the regiment was led by Col. MacKay. His company was indeed mostly made up of highlanders. On the other hand Lindsay's company was mainly from Angus, Fife and the south east of Scotland while Sinclair's men were a mix of higland & lowland men. Beaton's company was by comparison almost completely German with only a few Scots. The two finaly companies was made up of men from Aberdeenshire & Perthshire in one and Irish and Western Highlanders in the other.
After Breitenfeld Monro got permission to recruit any Scots, English or Irish he found among the prisoners but when these turned out to be very few he wanted to recruit Germans instead but this not allowed by Gustavus.
While there was a strong highland presence in the regiment it was hardly a regiment of highlanders nor did it's commanders view it as such.
The best modern day source for the Scots in Swedish service is James Fallon's "Scottish mercenaries in the service of Denmark and Sweden, 1626-1632" which is freely available from Glasgow University theses.gla.ac.uk/941