One thing I HATE about this meter: It beeps loudly anytime, anywhere. Several beeps on boot, beeps on every button press, beeps on ranging.
One thing I like about this meter: Even if the continuity beep isn't latched, it's fast and loud.
Removing the buzzer or wrap it in something doesn't cut it, because I want the loud beep when doing continuity.
Solution:
Turns out that the relays are high-side switched and in diode/continuity mode, only the relays K1 and K3 is activated. The other modes has other combinations, but K1=on, K2=off, K3=on, K4=off seems to be unique for this mode. So a simple diode AND-function could be used to only enable the buzzer in the diode mode. The buzzer rests at +6.66V and the relays are 5V-driven with respect to ground. So the LED is to avoid that current from the 6.66V rail (or whatever it is) creeps into the 5V circuits. Any red or green LED with a forward voltage of about 1.6-2V should do it. I don't think the component values are critical in any way. 1N400X or 1N4146 is probably fine, or even two LEDs for the "AND" (negating the need for the pull up LED). I just happened to have 1N5819 schottkys. The buzzer is dynamic, so no need for a "return path" or relying on the implicit back diode in the 2N7000, so a bipolar transistor will probably also work just fine.
If you want a quiet beeping in the other modes, just parallel the DS on the transistor with whatever resistor feels right (the buzzer is 16 ohms).
Here is the back side of the analog PCB. There is no need to remove the shield as the relay is accessible from the back side. Don't mind the blue LEDs, I just mounted them there in order to see which relays were on in which modes.
...and here is the "ghetto mod" itself.
It work very well, the buzzer is off in all modes except for diode/continuity. The instrument even "feels" more professional, as you now hear the relay switching when you change modes, something that the buzzer shouted down before.
Edit: So the "embedding" of the pictures didn't work. Sorry if the context got messed up, but you have the pictures below.
Edit2: Do'h! Naturally I misspelled "marked" in the schematics as "maked". Another thing to note, is that the buzzer itself has a +-marking and as far as I can tell, it was mounted backwards on the PCB. And yes, I damaged the plastic of the buzzer with my soldering iron as you see in the pictures...
Edit3: Clarification: The "positive terminals" on the relays refers to the *coil*, not any of the contacts.