G'day,
DougR, for what it is worth, I have been having a look at a short CV of Ken Curtis and whilst he began as a singer with Tommy Dorsey and Shep Fields there is no mention of him having been an accordionist.
I was looking at the IMDB Here
and for "The Quiet Man" , it shows that 'Galway Bay' and 'The Young May Moon' featured in the film too.
The background to 'Garryowen' can be found here.
Bcnu