Microphone replacement
As someone who designs pro-audio equipment for a living I can confidently say that this would be totally dumb.  Here's why:


No tech specs on the old mic.
No tech specs on the new mic.
No tech specs on the device that you want to swap mics on.
No mention on what performance levels you want.
Hand winding transformers for audio is difficult at best.
Measuring the voltage at various frequencies is only part of the equation.


Given your interest in VST Plugins, I am going to assume that you want pro-audio level of performance.  And based on your previous questions, I am going to assume that you are fairly new at electrical engineering (that's not a criticism, as we all have to start somewhere and that is after all why you are here).

Mic pre-amp circuits are difficult, even for seasoned EE's.  Doing a pro-audio level circuit (or even a consumer grade circuit) is difficult without good specs and the test equipment to verify that it is working correctly.  

Using a transformer for this is not at all advised.  Yes, that is how they used to do it "back in the day" but designing and building a transformer that works well across the entire audio frequency band is difficult.  I know many really good pro-audio EE's, but maybe only one of them could design this transformer.  You could buy a reasonable Jensen transformer that is designed for this, but it will cost you a minimum of US$100/each and probably won't have the required turns ratio.

If you want to do this as a learning process, and I highly approve of doing things to just learn stuff, this is still the wrong thing to do.  Modifying gear like this, when you don't have a complete understanding of what is going on (no specs, etc.) is just super frustrating.  You would be much better off just buying the exact thing that you need, and picking a different audio project to work on.  Otherwise you run the risk of damaging an otherwise good piece of gear, not getting the device you really want, and getting frustrated and abandoning your EE ambitions.  And that's never a good thing.