Hello Number 1

Does your mic have only a signal wire and a ground?  Usually there are two wires and a ground.

In this case you will need to add a pull-up resistor and a cap to bloc the DC.  This will require some experimentation to get the best component values.  Does the mic manufacturer have a wiring scheme suitable foir connecting the Shure brand wireless?  Ours would be the same.

Add the pull up resistor (10k is probably a reasonable starting value) from pin 2 to the hot wire in your mic.  Short pins 3&4 together and add a cap (10 uF is a good start) between them and the hot wire of the mic.  Connect the ground wire to pin 1.