Hi,
I really didn't understand what you are saying. And i don't understand what you are trying to do.
Here is what it is supposed to work:
1- If you have 1 shipping method only. (it shouldn't have any country restriction)
2- If you enable this option: VM Backend >> Configuration >> Checkout >> Enable Automatic Selected Shipment?
Then this shipping method will be selected automatically, and since there is only 1 shipping method available there will be no "Green - Change Shipping Method" button.
Is it working differently on your server?
Regards,
Support