12 volts to the camera would kill it, it and the GPS antenna is made to work with the 5 volts you will find in USB devices.
I do think the charger is made to handle up to 24 volts input voltage so it can be used in trucks too, but 12 or 24 volts they will be scaled down to the 5 volts the camera need.
If you wnt to do avay with the original PSU and the GPS antenna on the wire, thats no problem, any other USB charger will do as long as it can provide more than 1.5 amps to the camera, and the USB wire between it and the camera is of good quality ( there are a lot of dirt cheap USB wires out there that can be problematic to use not least if its a long wire.
You would want to use USB wires with all copper wire in it and not the cheap CCA ( Copper Clad Aluminium ) wires
You could allso use a BEC that allso will step down the input voltage to what ever voltage you set it to, i use a fjew of those in some of my RC gear, but then you will need to figure what connectors on the mini USB plug is + and - and then do some soldering.
If you want / need to have the camera on a long wire its easier to just make a additional ciggerette socket in the trunk, myself i just put in a 3 way of those in my trunk to power cameras "way" back in my doghouse sized Suzuki car.
That work good and i can use the PSUs that come with the cameras ( i have one of my X cameras in the back window )