I have gone through the records of the Nairnshire Constabulary from its re-creation (due to stringent Govt requirements and mandatory Govt inspection) in 1858 until the Commissioners of Supply were replaced by the County Council in 1890. The force was so small that every officer appointed in that period was mentioned by name in the Police Committee Minutes. There is no-one named James Finlay recorded as having been a police officer in that period.
The Nairn Burgh Police (at most two men) did exist until 1866 when it merged with the County force. The Burghs of Forres and Elgin, and the County of Elginshire (later Morayshire) did also have their own police forces. Elginshire/Morayshire (which by then had absorbed both the Burgh forces) and Nairnshire merged to form Moray & Nairn Constabulary in 1930, and in due course became part of the Scottish North Eastern Counties Constabulary in 1949. Following regionalisation in 1975, Moray (apart from Cromdale and Grantown) became part of Grampian Police, while Nairnshire (and Cromdale and Grantown) became part of the present Northern Constabulary.
Dave