A Teensy 3.5 would be exactly what you need to go on without a custom PCB. It has 27 analog inputs, two of them on the two analog outputs, makes 25 analog inputs remaining. One for each pot or fader, plus some extra.
The analog outputs can be used to control the VU meters.
The switches go to the digital inputs.
You will need to cut PCB traces and solder flying wires, but do not exactly need a PCB.
If the mixer is working, I suggest selling it and buying a ready-made controller. That would make more sense, ecologically and economically, than destroying a working device, so leaving it's footprint but removing it's functionality, and fiddling something without knowledge and uncertain outcome. Also one who buys this thing will not produce another footprint by bying a new one.
Plus: it is not only the soldering, but also the software, that needs to be worked out.