There are a lot of apps for changing the currency type in the Shopify App Store
These apps only change the displayed currency on the page. When the customer gets charged they will still get charged in the store currency, and they have to bear the FX risk and charges (ie they get charged in the store currency and then their credit card provider FXs to the customers card currency). Unless you know of any App that doesn't do this? As far as I know the only way to actually charge customers in different currencies on one store is with Shopify Payments. I am also in a non-Shopify Payment country unfortunately so have had to set up completed separate Shopify stores for each currency I want to charge in.
I think your only option (if you want customers to actually be able to check out in different currencies and not just see the prices in different currencies) is to run seperate Shopify stores, each with a different store currency. That's what I had to do, I have four domains, each with its own Shopify store and each with its own store currency. It makes inventory management and store updates very difficult but Shopify doesn't offer any other solution that I've found out about.
Hi! If multiple currencies are not available, it is better you run multiple sites serving different domains, with each domains allowing a different payment check-out. It is the best way to control differences among currencies, prices, products, shipping costs etc.
Among multiple websites, you may potentially use Geo Redirect to auto direct visitors to correct website URLs based on their geolocations by IP. Thus, customers can go to relevant websites and find useful product info seamlessly without getting lost. You can easily set up redirecting rules within a few steps. No code is necessary. Shopify platform is perfectly supported.
Hope it helps.