There is a copy of the book in the Scottish National Library, Edinburgh. Several of the versions of Scottish children's songs contained in it are also in the Montgomeries' Sandy Candy and some editions of their Scottish Nursery Rhymes with the same lyrics and musical arrangements complete with oddly shaped rectangular notes. This has lead me to the firm conclusion that the Montgomeries contributed to the Nicht At Eenie collection.
My notes say the following. edited by Rev A A W Ramsay and others (1932) Nicht At Eenie. Warlingham, Samson Press. No mention of any MacNab as author on the book that I recall - maybe he did the cover?