As Davd Hess said a while back, handheld meters simply aren't designed to have their battery terminals exposed when they are in operation, it's just not safe.
I have occasionally read stories where someone used a handheld meter to measure its own battery voltage. This is safe to attempt *if* the common lead is not connected to anything but if common is connected even to the negative side of the battery, bad things™ may occur like destruction of the meter depending on the design.
Bench meters have galvanically isolated input circuits for safety and performance reasons so they can get away with measuring their own internal voltages *except* for those of the galvanically isolated input circuits themselves. Tektronix designed the 7D13 DMM plug-in for their 7000 series oscilloscopes with galvanically isolated inputs so the 7D13 DMM can be used for troubleshooting and calibrating the oscilloscope that is is plugged into assuming that the CRT readout works; as I recall, some of their service manuals even do this but normally you would have some other meter available.
Some bench power supplies have floating outputs allowing either the positive or negative output to be tied or not tied to ground or any other reasonable potential as required; a Tektronix PS503 for instance allows up to 350 volts between ground and the floating outputs. One of these could be used to power a handheld meter but performance would likely suffer and safety certainly would. They sometimes do not support more than a few tens of volts of isolation so powering a handheld meter and then connecting the ground lead of the handheld meter to the 370 volt DC bus of an off-line switching power supply could be momentarily exciting. The same issue comes up if you remove the chassis ground connection between an oscilloscope and power outlet allowing the oscilloscope to make floating measurements.
Somewhere I have a "small" modular high isolation power supply which uses an air gapped transformer for 1000s of volts of AC line to regulated DC output isolation (and like 30pF of capacitive coupling) but it is not much smaller than most handheld meters and larger than some.
An issue which will matter in some applications is the common mode capacitive coupling. With a handheld meter in your hand, this will be about 200pF between common and earth ground. The high isolation power supply I mention above adds 30pF to this. A Tektronix PS503 which supports 350 volts of isolation adds 2000pF which will affect measurements of some circuits.