I'd agree: given our modern perspective, a WW2-era atomic pile is more convincing for game purposes than any sort of battery. Especially since we're talking about large cargo submarines, it doesn't even have to be particularly ahead of its time. (SSN-571 was authorized in 1951, launched in 1954, so there's only a few years of additional post-war design time.)
If you want to combine the Verne style with fission, then I see that there's 3.3 mg of uranium per cubic meter of seawater. Perhaps
these guys are rediscovering his technology. But it seems to me that somewhere on this planet of coral atolls, we'll need some mines for heavy metals, and that place will be politically and economically important.
Unless we want to put in a species of metal-concentrating coral. (No wonder it grows in big rings; the species that grew in dense groups all blew themselves up...)