You are indeed correct that while 2Checkout is a supported gateway in Georgia, the gateway themselves don't support GEL as a currency, which is a shame! https://www.2checkout.com/faq#what-currencies-does-2checkout-support
As a workaround, I would like to suggest that you consider setting up a manual gateway, like a Bank Deposit or a Money Order, and then you have the option to leave instructions for your customer (such as instructions on how to complete a bank deposit by offering your bank details) and they will see these instructions on the order confirmation page. Then you should choose not to fulfil these orders until you have confirmed that you have received the funds from that customer: https://help.shopify.com/manual/payment-settings/manual-payments
Hope this helps!