I bought my Nokia Lumia 625 online from Italy (WIND is the carrier). It is unlocked but I cannot update to 8.1 because the CYAN update is still 'under testing' for that carrier.
Does anyone know if there is another way for me to update to 8.1?
Currently, WP 8.1 and cyan are being shipped together for Nokia phones like your Lumia 625. There is no way to get the release version of 8.1 for it without cyan.
As @Cashchw suggested, I would ask you wait for couple of days as you’ll get Lumia Cyan firmware update first so you don’t run into any issues later. The problem is if you upgrade to WP 8.1 before Lumia Cyan, you need to wait for a Bitlocker and low memory space fixes that the WP team is still working. If you do other way round, you don’t have to worry about it then.
In case you are too excited to wait, you can get WP 8.1 and GDR 1 update by registering for Developer preview and follow steps mentioned here – http://dev.windows.com/en-us/develop/devpreview
Note: Register using Option 2: Build apps using App Studio -> free option