I have an UT61E multimeter, which uses 9v batteries but works perfectly fine with as little as 3v, though it shows low voltage at around 5v.
So I bought a 25F 2.7v super capacitor and built a small circuit using
LT1307 to boost the 1v .. 2.7v to 5.5v to keep the multimeter happy.
To charge the supercapacitor, I use a simple 1117 linear regulator which charges the supercapacitor from USB (5v) with 2.65v (to keep the voltage below the supercapacitor's maximum 2.7v and the linear regulator has an internal current limit of around 1.2A so the USB ports aren't overloaded.
It takes about 1 minute, maybe a bit more to charge the supercapacitor and then I can disconnect the multimeter from usb and it will run just fine for more than 30 minutes.
This could work for you but with my solution, you'd have to remember to always disconnect the meter from usb when you want to do measurements with mains voltages (as the ground of the meter would be connected to the ground of the usb). There are power isolator chips like
Adum5000 for example which would fully isolate the meter but add to the price.