The first thing to do is try to figure out why the mic doesn't work, even if you just want to gut it. Since it's a dynamic, there are only a few parts: the capsule, the transformer, a switch, and the connector. I see that this mic has a dual impedance switch, so the transformer will have a few taps.
Get yourself a multimeter--Radio Shack has a $16 jobbie that works fine--and test each wire for continuity, and test resistance between the transformer leads. If all is well, then maybe the capsule has died a horrible death, which is rare, but it happens.
Probably you will find there is a broken wire. Resolder it, and see if it works.
Now if you decide you want to gut it and start over, you will have already learned all its parts, and more importantly, you will know exactly how much room inside you have to play with.
Then you just have to pick a mic design!