If the scale doesn't like NiMh cells, than it probably doesn't like the fact that you are offering it 3.75 volts instead of 4.5 volts. Generally scales end up using highly regulated voltage internally, so they need 'headroom' on the supplied voltage. When fully charged a 4.2 volt Li-Ion may offer enough 'headroom' for the regulator, with key being the word 'may', 4.35 is more likely to work, but neither is likely to work for very long since somewhere r before 3.75 volts it will stop working, and 3.75 volts is well above complete discharge voltage on a Li-ion cell voltage. The scales are often not very high current applicatrs. Some of them will run on CR2032's, which is a 3volt low current battery, but obvious not your scale.