Will my save game still work as normal? (I'm in the southern hemisphere if that matters).
And would changing my system settings be enough, or should I change my nintendo account information as well for this to work?
I once changed the settings from "North America" to "Europe" and it changed nothing except the language (and the time if you choose to play with the current time of the zone)
I'm not sure what changing the region in the system settings does, but if you change it in your Nintendo account, be aware that you lose all your eShop funds (including gold coins) due to switching to the new region's eShop as well.