Looks like there are some multimeters that can and some that can't. I'm replacing the shutter on my camera. If this doesn't work I'll build a discharging tool. Here's the multimeter manual:
Discharging tool with resistor is much better choice. Meter is generally not recommended for this purpose.
Capacitor usually discharges on it's own after 10-20 minutes.
The idea of a multimeter is to have a high resistance, but this can still be too low. Some multimeters already trigger an electronic flash by just trying to meter the´voltage at the trigger capacitator.
But for metering the voltage at the main capacitator any multimeter is apt. You will see the voltage will have likely already leaked before you meter.
(That thing with the trigger capacitator is weird anyway, I shall have to investigate on the value of meter leak-currency and triggery-currency to go to the inductor. One day...)
Reminds me of the time I 'tested' the exciter coil in my sensitometer. It was over 1000v and it really did fry my cheap multimeter. It did not blow the fuse because the current from a spark coil is very low.
The standard voltage at the capacitators we talk about is about 350V DC. The range of common multimeters is by far larger. All my ones for instance meter up to 1000V.
There is no harm in using the 375 in DC voltage measurement to discharge the capacitor. The advantage is that you can actually see the remaining voltage in the capacitor and know for sure when it safe to touch the capacitor. The disadvantage is that the impedance of the meter is too high about 10 megaohms and thus it would take longer to discharge as compared to a 10 kiloohms resistor. And yes the 375 is rated for 1000V and I have used it to measure up to 500VDC
The 375 actually only measures up to 600V but can take 1000V without damage.