Success! I've got it disabled by cutting one track and running a wire.
The track to cut is on the LCD side of the PCB. You need to remove the battery door (2 screws), the 4 case screws, and then 6 screws that hold in the PCB. There are 2 screws that hold in the LCD, so you don't want to remove those. The LCD screws are the second set down from the top (LED) end of the meter.
Here's the track I cut (circled).
Pic 1:
...and here is the wire I ran.
Pic 2:
The anode of the diode D8 goes through the rotary switch to the 9V battery positive. It's connected for every rotary switch position except the middle (OFF) position. This seemed the easiest place to tap it off after the switch.
I ran it to the common pin on U4, which appears to be a FET. This is where the cut track runs to, and is where the non-contact AC detector circuit gets power.
I've tested it and am happy with the result. The non-contact AC detection works fine as long as the switch is not in the OFF position (doesn't matter what mode it's in), and all other modes work (see note re: Buzzer).
Note: If you cut the track but do not connect the wire you will have no buzzer, even for the buzz test mode. I wasn't willing to take components off the board to figure out where the track ran. Anyway, this stops the unit "squawking" when the battery is low (which just makes the battery flat faster - and really annoys airline security staff, let me tell you!), which I've heard it do even when the switch was in OFF position. As a consequence, I'm expecting to get a lot longer battery life out of it now, and annoy a lot less airline security.
Anyway, hope this helps someone.
Have fun!