It isn't "soldering cable", it's not even "cable". It's just standard "wire" that's been soldered to the batteries.
Those look like 'AA' batteries, so that's 1.5v x 3 = 4.5v total.
A length of insulated wire stripped out from some domestic electrical flex can safely handle that
That's assuming it's just for the batteries, there must not be any high voltage/mains voltage involved whatsoever).