In some instruments vibrational modes on the body are essential to radiate the sound. Examples would be a guitar, drum, violin, banjo. In these instruments materials will have a much greater impact on the sound since material density directly affects resonant frequency.
I think the concertina is not in this class of instruments since the sound mainly comes from the reed itself. It will, however, be affected by the absorptive qualities of the material inside the concertina. Also, after watching this I was surprised at how similar a metal and wooden clarinet sound.