"The only thing I know about the cable is that it IS coax and the outside
diameter is about 3.75mm. Since it's from Europe, is there anyone from
Europe who knows coax specs and what this cable is likely to be, so I
can get the correct connector? Or does it really matter for this
application?"

Size does matter. Coax crimpers and the connectors depend upon a certain
size of coax. If you are measuring the outside diameter including the
rubber coating, then the coax is smaller than RG-58. It would certainly be
50 ohm coax, so that is not the problem - but there are certain crimped
connectors that would be tolerant of the difference in size. The problem
with crimping is that there is a different die for each connector size.
Some crimped connectors might not work with a coax different than intended.

Good luck, Colin