I wouldn't just try to knock up a facsimile of the microphone shown in your link without specialist advice. Some issues you'd encounter include the problem of eliminating specific wavelengths around the 60Hz mark which would cause a noticeable hum. The hole size in the mesh is critical in order to prevent such wavelengths entering the mike in the same manner as the mesh size in your microwave oven hinders the escape of microwave radiation. Also, try not to use brass mesh as you're looking to make what is essentially a Faraday Cage around the mike elements. Copper mesh is far better and can be painted if necessary.
Without being aware of your expertise and knowledge of radio/electronics, it's difficult for me to point you in the right direction. However, as I said, knocking one up without some guidance is prone to failure. I'd recommend you ask the guys on the forum I provided a link to.