Can I create an external checkout page to accept multi-currency for my store?

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Hi everyone .. I need your help!

I have an online store in a country that does not support Shopify Payment. I'm selling in more than one country and I need to be able to show different currencies. As you know, Shopify checkout page shows the default currency of the store only and does not allow any customization. 

Can I ask a developer to develop a checkout page outside Shopify that can read the cart, process the payment using any payment gateway, and then redirect the buyer to my shopify store again?