Using the same gauge wire as what Honda installed is the safest bet.
But, note it has a high strand count as robotic wire has. The thicker each strand is, the more susceptible to bending and vibration bending fatigue breakage.
Try to find a wire chart that includes a temperature specification, and note that wire in a bundle won't run as cool as those hanging in free air.
Plated wire is used to preserve the copper from corrosion (which would making it thinner or narrower in cross section over time). The plating is sacrificial. As in, it will corrode and oxidize prior to the plated core. The plating is not in and of itself much aid to carrying electrical current. It just prolongs the life of the core wire.
The lithium battery has no effect on choice of wire different from stock. If battery is rated for ~210 CCA, it will both deliver and receive such current without harmful effects. But, that is controlled by the voltage potential available at the terminals. You can't push current into it without a higher voltage potential than it has statically. And that is why you need a voltage limiter for the battery, (that most call a regulator). It is there to keep from putting more energy into the battery than it can safely store.
One caution. Most of the lithium types have a spec in the warranty about over depletion voiding it. That means if you leave the key on and or lighting, the battery can be damaged by a deep discharge. Lead types can be damaged by this too, but it is much more forgiving of such abuse. Lithiums are less reliable to recover from this. Most other electronic devices that use lithium type batteries monitor for too low voltage and disconnect it to save the battery from harm. I know of no such device available for the SOHC4.
Cheers,