DIY Wireless Gaming Mic/Headphone Pendant

I want to create a relatively small pendant that I can connect a pair of headphones and a mic to (both using 3.5 mm jacks) which communicates to my computer over either Bluetooth or WiFi. Since it’s for gaming/media, it would need to be relatively low latency. I got the idea because my current wireless gaming headset (Logitech G930) broke, but I have been unimpressed with the quality of the headphone and the mic of the headset itself. I figured, why not just have a pendant that I can wear around my neck to make any headphone or mic I have into a wireless one. I’ve Googled around and couldn’t find anything in the market (I’d like to think my google-fu is somewhat thorough).

I am tempted to just take apart my G930 (the only thing broken is the actual head band, but the dang thing is pretty uncomfortable anyways), find where the mic in and audio out wires are at, and just solder a 3.5mm jack to each of those. But that would leave me with a ton of extra bells and whistles on this thing when all I really want is a low latency transceiver, plus it’d be interesting how small I can make this if I made this pendant from scratch.

On to my question:

Should I use WiFi or Bluetooth? or some other protocol I don’t know about? It’s been explained to me by a friend that A2DP might not work since it primarily handles one-way audio signals (as in, I can transmit game sounds to my headphones, or transmit my voice to the computer, but not both at the same time).

Thanks in advance,

Kert