Ignore the Tannahill Weaver's version as it strays away from the melody in the second part of the tune, (I don't think the singer had the range). In all the old, Victorian, printed versions of this melody it is written in D major and finishes on the 3rd, i.e. F#.
If you play in this key, just switch between D and G and the "funny" bit I suspect is the second half of the penultimate bar where a G minor fits .. it does on the piano.