Hello Erik,
I haven't got any Ms anymore but the IIIa you mention is easily the quietist of the ltm cameras I still have and certainly quieter than the M6 that I used to have, I can barely hear it. What is more the 1-20 timer is almost inaudible. The sound is deadened somehow.
I remember discussing this with the man who used to work on my cameras who was a master of low shutter tension. He couldn't offer a plausible explanation. It had previously belonged to the Royal Ulster Constabulary and came to us in poor condition.
Film is currently in the III, black/nickel of course, the one I have had since 1965.
Michael