I've compared the two versions and I agree with your colleague for the Tannahill Weavers' version.
The Fisher Family version, led by Ray and Archie, has a slight variation in the chorus part:
G      C                   Em
Sing ye o' the Cuillins o' Skye
   F          G          F G
O' Harris, Dunvegan, Fair Iona,
C         F             G
Joy of my heart, Eileen Mulligh.
          C
Whether I wander east or west,
G                            F   G
Waking or dreaming, thou art near me
C       F             G
Joy of my heart, Eileen Mulligh.


Robyn