the voltage can stay 6v but you dont have enough current to power your device .
the littium dont drop in voltage until they finally collapse , the same is with ni-mh they stay 1,2 v until 99% of their capacity , the meter can still read 6 vor 4,8) with nimh while there not no enouth juice( power) in the batteries at all .
the regullar alkaline , go down very fast down in voltage under load , so it can be that even you use 4 that give you 6 v on open circuit they will very fast go under the minimum that usb need ,so actually you will not use all the capacity from the battery.
http://www.nimhbattery.com/delkin-rcr-123a-rechargeable-charger.htmyou can use these ( you need 2) in your box , the benefit of rechargeable lithium ion, they dont have big self discharge curv, less then 10% per year , so you dont have to remember to charge it if you did it ones and dint use it , the ni mh must to been charge every time before use since drop very fast in self capacity( the v stay 1.2)