Update: If you sell in local currencies and have access to 1-page checkout, customers will checkout in the currency that you've set for the country of their shipping address. If a customer chooses to ship to a country or region that differs from the one that they selected on the storefront, then the currency will change to match their shipping destination at checkout. Your customers will see the total cost of their purchases in their local currency, including currency conversion fees.
Learn more about local currency checkout behavior in the Shopify Help Center.