Unfortunately the easiest way to resolve this is to copy the msshrtmi.dll file from:
C:\Program Files\Microsoft SDKs\Windows Azure\.NET SDK\{version}\bin\runtimes\base\x64
I know it's not very nice copying DLLs around, but this is the only one you'll need to prevent the error, and its tied to the SDK version you're using, so won't change until you update the SDK.
A viable alternative would be to add a config value in appSettings
and apply a config transform when you build the application for Azure.