Ted here from Shopify, thanks for reaching out to us!
Based on your location, you should be able to connect to any of the gateways mentioned in this guide. Paypal, Razorpay, 2Checkout and CCAvenue would be the most popular gateways to connect with. If the gateways listed in the guide require further business documentation as you've advised, you could consider using the Advanced Cash on Delivery app instead. This app provides your customers with a cash on delivery payment option when purchasing from your store; more details regarding the app can be found in this guide.
Alternatively, you can reach out to any local third-party gateway provider directly (such as these gateways for example) and ask them if they have a private plugin available for e-commerce platforms such as Shopify. You could then install their private plugin to your Shopify admin instead.
Please let me know how this goes! How are you finding Shopify so far?
Thanks a mill,