Finally I ended up buying som NiCd batteries with solderlugs. I didn't buy the more expensive C-size ones, but the cheapest ones that would fit, which cost about 24€. The DMM seems to be quite good, so I figured it was worth the new batteries.
Installing wasn't more difficult than soldering the old wires the the new batteries and now the DMM works great, both on AC and battery. The new batteries are specified to almost the double amount of charge, so I expect the DMM to be going for quite some time between charge.
|Measuring voltage running on battery power|