Although the query has been raised long ago, answering this for the benefit of others who might land on this thread.
Handling FedEx international shipping with Shopify can be done using an app like FedEx Rates, Labels & Tracking app. Since you do not need real time shipping calculation, you can disable that in the app. The app lets you print FedEx labels and invoices and also helps in FedEx tracking.
You will also be able to handle duties and taxes payment within the app.
This is quite old but i would still like to mention my comments here as it may help others. You can give flat rates and still print labels with Shopify's FedEx integration. Have you started using it? Ideally you should not face any problem. However, since you mentioned international shipping, i was wondering whether you are using harmonised code? If yes, then you need to use the Multi Carrier Shipping label app that has a place for you to put the cod at product level and not face any problems at customs.