If you use piggy-back spade connectors on the wires from the buzzer you can connect and remove it simply by unplugging spades, no cutting or soldering of wires.
The first type of buzzer I tried is this 'electronic' one below that I had first used many many years ago as a 'lights on' warning. However despite being 'electronic' it uses a very crude mechanical sounder which sounds horrible - bearable for the lights on warning as you either shut the door or turn the lights off, but not for the something that is going to be beeping at you all the time you are waiting at a junction:
Better sounding are these 'piezo' type, small ones are 5v so you use a series resistor, but there are larger 12v types:
If too loud when stationary they can be quietened with a series resistor to drop the voltage, or even wrapping a bit of sponge round them. But given the characteristics of the MGB you are quite likely to find a volume where it is too loud when stopped and inaudible at speed!