Is there any problem with soldering a charged battery?
Please, practice some engineering safety skills and first use a multimeter and check the voltage level of the battery. If it's a single cell Lithium Ion battery, it will be between 3-4.2V with proper charge, and &lt;3V is getting on the low side. 
It can still discharge some serious current below 3V though, so perhaps next time use isolated equipment and/or gloves/tools. Remember to use some kind of eye protection in case they do actually explode from heat or expansion. Use leaded solder if possible, and if you have temperature control on your soldering iron get it as close to 260-270 degrees Celsius as possible so that it will melt the solder but hopefully do less damage to the batteries.

You will have no problem as long as the positive terminal does not short with anything. Perhaps (while not grounded yourself) put some electrical tape around the positive terminal/wires and make sure the PCB is safe, the ground wire is soldered and ready, and then you may carefully use tweezers or something on insulated wire to position the exposed wire and solder it to the PCB pad or whatever you are trying to do (you fail to mention what setup you have, how it all connects, and what you were doing when it actually shorted and burnt you other than you took the eGo-T apart).

Maybe use a plastic/insulated vice to hold the item while working on it too.