That mic (a dynamic, I think?) is one that was supplied with the better quality model Sony mono portable cassette deck of about the mid '70s. The small diameter plug of the connector is indeed for the "remote" function, which merely allowed you to use the switch on the mic to turn the cassette deck's motor on and off (when you were thinking what to say next, or waiting for someone else to speak, for example). The mic's connector, the larger diameter one, is unbalanced.
I would just use an ohmmeter or continuity tester to figure out which pair of wires, on the cut-off connector, goes to the small diameter plug (and/or the larger one too, actually). Then you can match the wire to the one(s) coming out of the mic and know which is which.
I remember using that mic with its cassette deck, and it was pretty good for what it was. It would be interesting to hear what it was like into a real recording machine!
Cheers,
Mark W