Hi,
I would like to offer you my expertise in the field of digital and analog electronics, PCB design, embedded firmware and software development.
As you said there are few ways to approach to your project, and the best way depends on what exactly you need. Here are few question:
1.) What is expected quantity to be produces?
2.) Should price per unit be minimal or it is not important?
3.) Is the unit battery powered and should special care of low power modes be taken?
4.) What wireless technology would you like to use? Bluetooth, Wifi, LoRa,..
5.) What is microphone used for, would audio be transmitted via wireless? or would audio signal processing be done on unit?
If you could answer these questions, I can suggest you the best approach. Raspberry would be easiest to develop and development cost would be smallest, but price per unit (BOM )is high in that case, it is not low power and battery operation is poor, it has problem with mass production and user experience is somewhat degraded.
Other option would be custom made hardware and firmware, which would solve this problems, but development is trickier. I am fine with both, depending on your preference.
Thanks,
Vladimir.