Your registered country doesn't matter. Submit ID in your name is all that matters. It doesn't need to be from your registered country.
Also you can change your registered country by submitting proof of residence in your name (utility bill such as electric/gas etc).
Volte 80 Frost DK--Cycloneduke 80 Holy Pally--Moardotz 80 Desto Warlock-- Dexterworgan 80 Assassination Rogue----Liadon 80 Feral Druid--Mumbles 70 Frost Mage--Bibleblack 70 Disc Priest--Dylli 70 DM Hunter--Krosa 70 Fury Warrior -- Slapntickle 70 Prot Warrior -- Okoi 80 Enha Shaman + 4 slave shamans multiboxed to 70 - Darksorrow EU PvP
There is no other way other then getting your phone back or mail them some ID, the country you are from is irrelevant, I have my country set as UK so I can take advantage of all promotions, but I'm not a British citizen.
However, if you added an authenticator to an account that wasn't yours to start with and that's why you have no ID to give them, good luck finding your phone, otherwise you're about to face an uphill battle.
The mobile one can get lost as well, you can format, people can also get a hold of it. But it's easier to backup, and you can have it on multiple phones too. In my case, I just made a Titanium Backup(Android phone) of my authenticator, and have it on an encrypted .rar on my Google Drive, so it's accessible everywhere if I lose my phone.