What happens if the store doesn't support the currency set for a given country?

Shopify automatically converts the shipping cost to the checkout currency. What matters is the currency you choose for that country in the app - not the country’s usual currency.

For example: if you price Hungary in EUR and your store supports HUF but not EUR, the shipping cost is converted from EUR to the currency the buyer pays in at checkout. If you price Hungary in HUF and the store supports HUF, buyers see exactly that amount, with no conversion.