I'd imagine that risk, if it's present, is from capacitors inside the meter. Capacitors inside tools and appliances can hold a large charge for a relatively long time, even after the circuit is no longer externally powered.
You can discharge a capacitor by shorting it with a screwdriver (with an insulated handle), or by clipping a resistor to the capacitor leads for a less abrupt discharge. I think people who do a lot of appliance repairs learn to look carefully for capacitors when opening appliances, and make sure that any moderately large ones (or ones that there was reason to believe could have been charged to a high voltage) are discharged before beginning work.
I don't know how common large capacitors are in multimeters. I think there's a much bigger risk when opening a CRT monitor or a microwave.
After unplugging the power cord, I always switch the device back on with the main power switch. That should be sufficient to discharge the caps. It's never been a problem. Other than that, I just avoid touching anything close to the power circuitry. And, finally, I've survived many 220V shocks as a kid when playing with retired washing machines and such (I don't recommend it), 110V should be less shocking. :-)
You generally only have to worry about capacitors being charged still on tube-type gear (anything with high voltage circuits), anything with solid state parts, will self discharge within moments. This doesnt have a motor starting cap, or high voltage, so the risk is near zero.
You can discharge a capacitor by shorting it with a screwdriver (with an insulated handle), or by clipping a resistor to the capacitor leads for a less abrupt discharge. I think people who do a lot of appliance repairs learn to look carefully for capacitors when opening appliances, and make sure that any moderately large ones (or ones that there was reason to believe could have been charged to a high voltage) are discharged before beginning work.
I don't know how common large capacitors are in multimeters. I think there's a much bigger risk when opening a CRT monitor or a microwave.