I got a lead to a former Caithness engraver, Helen MacDonald, from another post and sent her an email. She has just got back to me to confirm that the initials "JMM" belonged to John McDonald. An extract from Helen's email is attached:-
The initials JMM belong to John McDonald, he was an engraver with
Caithness from 1969/70 until about 1980. He used to live in John O'Groats
and was a real character, always doing practical jokes on us all.
I'm trying to make up a list of Caithness engravers but it is taking me
longer that I thought. I will check it all out with Willie Bain (another
caithness engraver) to make sure it is all correct.
Hope this is of some use to others