I do not suggest any use of lithium ion cells , they need special circuitry about charging that you do not have one.
But hey I got confused again ... are you thinking to rebuild the original pack ? ( My suggestion to it its a big NO )
Or to make an alternative battery pack completely external ? ( Yes with common batteries like NiMH AA but you will need many of them,
and the 2700mA version does not come cheap.)
About making the battery pack , you are alone on this , as concept.
Its best before you go for shopping , to make an schematic of what you have in mind and post it here ,
so to get an advice .