Those mikes were built for a PA system, probably. The internal hookup is different from the mikes the Astatic book is meant to be used with.
Good chance that there are TWO wires inside the braided shield. If so, it was meant for use with a low-impedance head like the DN50, and NOT the round high-impedance head.
The internal schematic would typically be found glued inside the bottom cover. Good chance that this mike has only a "transmit"-side switch and does not have a contact that makes the circuit for receive side.
The round "lollipop" head is normally built with a high-impedance cartridge. Very few solid-state radios will match this mike, because they'll have a low input impedance. Even if you get it to key the transmitter, the audio will be incredibly weak.
The DN-50 head is a very low impedance head. It's meant to use with very long cords between the mike and amplifier, with a step-up transformer at the far end. Might sound okay with a solid-state radio, or may be a bit on the weak side.
Removing the switch from inside the mast is the only way to find out if you have any 'spare' contact points in there to wire up for receive side. Lining up the screw holes on the switch is a major PITA when you reassemble it.
73