A voltage issue: no.
An amperage issue: Maybe.
A cable issue: Be careful.
The voltage will be determined entirely by the wall-wart/charger you're plugging in to, so if you're using a korean charger, you don't have to worry about voltage.
The thing to keep in mind is that different chargers will provide different amperage levels. Some older chargers might only provide around 500mA (milliamps), whereas more modern ones can provide up to 3000mA. Using a higher amperage charger won't blow your device up or anything, but it miiiiiight affect the overall lifetime of the device. Since the Famicom Mini is relatively(?) new, I don't think you really have to worry about it. I'm sure there are specs listed somewhere that say what the ideal mA would be, if you're paranoid and want to make sure it matches the mA provided by the charger as closely as possible.
One warning, though: Even if voltage isn't an issue and amperage is only a slight consideration, the cable itself is definitely something you have to be wary of. I assume the Famicom comes with its own cable, but if it doesn't or if you ever need to replace it, try to make sure you're getting something you know for sure will work with that device. I don't know how much it applies to USB mini, but using the wrong USB-C cable absolutely can bork a device.
If you want to read some tech-y stuff about USB cables, power, and charging, this might be of interest:
https://www.extremetech.com/computing/115251-how-usb-charging-works-or-how-to-avoid-blowing-up-your-smartphone
