I successfully created a speaker/microphone/transmit button circuit for the puxing 777 which probably works for all puxing radios. Instead of simply using circuits found on other websites (always for other radios), I decided to reverse-engineering an earphone/microphone headset that came with the radio to determine how it worked. I can't claim that I'm an expert in electronics theory, but I can say that I faithfully rebuilt the circuitry within the factory-shipped headset and it worked. The result allows me to leave my handheld radio in its charger while casually listening/transmitting with a button that I made instead of having to reach around and awkwardly squeeze the transmit button on the side of the radio. Once again, I built this circuit and it was successful for me, but there may still be a better way to do it.
The microphone is a 20-cent electret microphone with no special modifications. The speaker I used is a standard 8ohm loudspeaker with no special modifications. The switch is a keyboard-style (push-to-talk) switch, and the capacitor I used is good for 10nF.
If you have any ideas for improvements, let me know! I'll post some photos once I have my completed little "base station" set up. My ultimate goal is to turn an el-cheapo handheld VHF radio into a decent desktop transceiver by combining it with a nice antenna (located on a balcony at 30ft) and a convenient, easy-to-use switches/buttons/microphone/speaker/etc on a desktop panel.