Your transistor circuit drawing should be red "I have an idea of inserting a transistor and maybe also some other parts to do the switching. Thus I have already invented the essence of the solution - that's a transistor and maybe also other parts connected. Now I need only someone to do the non-creative part of the design job!"
Unfortunately we know nothing what's the type of your original mic and which kind mic you are going to insert to the jack. Most of us probably would guess you have an electret capsule on the board. If that guess happens to be right it should be possible to use a jack which has switches and inserting to the jack an external electret capsule would replace the original one.
Making another mic type to work needs much more complex, but still successful guesses. Or some reverse engineering of your board. Something like Shure SM58 placed with jack switches in the place of the original can work, but more likely it doesn't because electret capsules have a DC circuit and the available audio AC voltages are also different.
Placing another electret capsule in parallel with the original has chances to be successful. But you very likely must somehow shut mechanically the hole of the original mic to stop it catching noises.
As said above, electret capsules make a DC path. You could feed the DC of your original mic through a mosfet or bipolar transistor, say through part X in the new circuit. The external electret mic uses also some DC. That current could be used to turn off X. The construction probably is simple if you allow 2 transistors, but it's impossible to draw it right nor calculate the needed resistors without having your board in one's hands for reverse engineering the mic input circuit.
A proper schematic of your board would reduce radically the need of guessing. I'm afraid the moderator closes your question if you do not soon provide any information of the actual circuits on your board.
