That sucks! How frustrating.
Couple of ways to proceed.
Hopefully you got a "battery power supply cable" with a 6mm barrel and croc clips". If not then you should complain to whoever you bought the charger from and see if you can get them to send you one.
If you do have one then you can use that to fix the 6mm end (at least for now). Then you can use someone's car 12v battery to charge the battery. It can be in the car but if so keep a close eye on things. You don't want a lipo gone wrong spoiling the shiny paintwork. Maybe use some car jumper cables to get things away from the car.
If that is not an option, you need to decide if you are prepared to give up on the possibility of returning the power supply if it doesn't work or fails. If you are ok with that then with the power supply disconnected from any electricity, you can cut off the 5.5mm barrel from the power supply close to the barrel (leave 3 cm or so on the barrel in case you want to use it again), strip back the two output wires connected to the power supply and use the chargers croc clips to attach the power supply to the charger.
Make sure to get the voltage polarity correct since the charger may not have polarity protection and you will damage it if you get it wrong. Generally one of the two wires has a white line or some marking indicating it is the +ve. A volt meter helps. If you don't have one this might not be a good idea to do.
Before you plug the power supply in to the mains, remove the barrel from the charger. Then apply the mains power and check the polarity and voltage at the barrel with a voltmeter. The center pin should be +12v. I'm assuming the outer barrel is -ve and the pin is +ve but check before you connect anything the mains.
It is essential you don't let the two bare wire ends touch so use insulating tape to separately around each croc clip and wire end. If you don't have insulating tape, you could use regular clear tape or masking tape as a temporary measure. Its better than not taping at all and this is just 12v so not directly life threatening.
If you have a soldering iron you could cut off the croc clips too and solder the wires together for a permanent solution. best to use shrink tubing if you do that.
If you don't want to cut the cord(s) yet and/or you don't have a voltmeter, then you need to find a metal wire that will fit in the socket of the power adapter's 5.5mm barrel connector. Some solid copper wire would be best. A small iron nail would work. It needs to be a good fit and not touch the barrel. This will expose the center 12v and you can connect the -ve croc clip to the barrel and the +ve croc clip to the wire. Tape them up separately to prevent them from touching. I'm assuming the outer barrel is -ve and the center is +ve but check before you connect anything the mains.
This should get you going. Keep a close eye on everything while its plugged in to make sure it doesn't fall apart and short out. That could cause a fire.
Afterwards...
Go buy a cable with a 6mm barrel and appropriately sized wire (pre-made or parts), get a soldering iron, solder and some shrink wrap (or insulating tape - good to have anyway) and, at your leisure, make the temporary fix permanent.
..or buy a different charger with the correct barrel connector.
