Well I can guess a rechargeable battery would be a good idea, as long you you are ok opening and shutting where you site it, and as you have to open for a normal battery no issue.
If you have a rechargeable I would have two, one ready to use and one on standby charging, so if it runs out your not left waiting for it to power up. Rechargeables are no less safe than usual batteries. in fact if you have solar panels they are a bonus as you charge when sun, and can use when no sun.
As for gauge, well that all depends on the draw of the battery,and there I have reached the limit of my effective usefulness, try searching the net, put your loco + rechargeable battery and see if you get a hit, or g scale and rechargeable battery,+ the battery power and draw and add wire gauge and see if you get hits. THEN if you get a reply see if you can find a second to confirm it! never resort to telephone wire! look in screwfix site and look at the wires for sale they may say what they are used with and solve your problem from the other end!
If all else fails ask on a model plane site because those guys tend be pretty switched on, flying your model is risky and avoiding a crash ensures they take care! So if they use the same battery it is likely (not guaranteed) that it MAY work with a loco, also rather expensive so check before transferring info from one site to another!
As you can technically minded I am not! but these thoughts may help you track down your answers, if not sorry for wasting your time.