Well, the good news is that, providing you can fit a small TRS socket into your headphones - they are often 'switched'. That is, when nothing is plugged in, the pins that are normally connected to the plugs tip and ring, are connected to two other pins. That was used for a long time on tv's with a headphone socket, or in small portable audio system. So as soon as you plugged in your headphones, the speakers would go silent - because their signal would now go through the socket, into the headphones. This would negate the need for an actual 'switch'. However, if you can't find a 'switched socket', then a simple 2-pole switch will do, be it a toggle or a slide switch.
So you would have to wire the wireless part to these two switch pins (getting polarity correct, left/right). When nothing is plugged in, the audio from the wireless circuit/headphone drivers will go straight through the socket, and it will behave as normal.
When you plug in a stereo plug (TRS 3.5mm) it will disconnect the audio signal from the wireless part, and connect direct to the plug. As to what the other end of this cable plugs into - that is up to you. I am assuming that the speakers in your headphones are standard 16/32Ohm types here. Often the red/white phono jacks are 'line out' and may not be able to drive the speakers in the headphones. (note, the 'line out' on soundcards has a built in driver so it can power headphones direct)
As for the ground wire, I don't see any problem connecting the ground wire permanently to the ground of the TRS socket. Each of the headphones speakers ground wires will most likely be connected together at the circuit board of the wireless part anyway. Just tap that and that is the ground of the TRS.
I can't find a decent picture of a socket... but one like this is fully switched, small, and would work:
**broken link removed**
here's another one with a small schematic showing the switching
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Sorry for spamming links.
There are so many types of socket, PCB mount, panel mount, solder tabs etc... all depends on what you can get hold of, or where you would prefer to get one.. ebay, mouser, etc..
So, two options:
1. Standard 3.5mm socket (preferably panel mount so you can mount it with a hole in the headphones). With 3 pins, tip, ring, and GND. Use a 2-pole (DPDT) switch that will switch both the left and right from the wireless part, to the socket.
GND/ground can just be wired to the common ground of the speakers. I can provide a crude diagram if you wish
2. Switched 3.5mm socket. This will have 5 pins. tip, ring, tip-switch, ring-switch, and ground. Slightly more complicated, but only one part. The trouble with this is, only way to 'switch' between wired, and wireless signals is by physically unplugging the cable. The first option might be better if you have the cable from your headphones plugged into one thing, and the wireless part in another - flick of a toggle switch and you can switch between those two inputs.
Sorry for a long post, sometimes even simple idea's can balloon with options, plus I prefer to explain things thoroughly, don't be put off!! I just repeat myself lots.