Fix balls machine

[Marcixxx]

I bought on ebay a broken balls machine.
I welded rusted and loose wires
Now the machine works but the 2 batteries (PowerSonic F1 1270 PS, 12V, 7A) are exhausted.


I thought of two solutions:
1) Buy two new batteries and a smart charger (original £ 35) or fast/smart (original £ 60) (supplied one is normal charger and don't shuts off the power when the batteries are charged, so after a while the batteries fails).
2) Connect an "external ac power supply" (original £ 79) and keep the exhausted batteries.


Do you think that the prices of the accessories are good or are can be find good quality/cheap compatible accessories?


Can someone suggest which electrical characteristics must have a "smart" or "fast / smart" compatible charger or a compatible "external AC power supply"?
The original charger is a class2 transformer:
input: 230 vac, 50 hz, 39w
Output: 13.8 Vdc, 1.7A


a last question:
Does anyone know what happen if i use the normal charger as external AC supply (with exhausted batteries), instead of the external AC power supply that is usually separately sold?


Any suggest is appreciated.
Thanks.