As a Microsoft Azure services client, I received earlier today the following mail: http://aka.ms/Qga48e.
I was wondering how I could migrate my Blob storage without
I don't think that it would be necessary. Besides Azure Blob Service and Azure File Service serve different purposes all together and the things you could do with blob service can't be done through file service.
As mentioned in the newsletter, what you should try to do is upgrade your client applications to make use of latest version of storage client library. If you're using an older version of library (< 2.0), there would be some pain in migration but migrating from 2.0 to 4.x (currently latest version) should be rather painless.
Next thing you should look into is the default service version of your storage account services. If you're using .Net storage client library, you can fetch it via GetServicePropertiesAsync method. You can update the default service version using SetServicePropertiesAsync method.
You may also find this link helpful about understanding storage service versioning: http://msdn.microsoft.com/en-us/library/azure/dd894041.aspx.
UPDATE: 13-DEC-2014
Azure Storage Team has published a blog post which talks more about this issue: http://blogs.msdn.com/b/windowsazurestorage/archive/2014/08/05/microsoft-azure-storage-service-version-removal.aspx.