Yes, you can run as many shipping modules as you need.
The key is in selecting the most appropriate module for the desired purpose.
Shipping modules can be configured to be ACTIVE for specified zones only, and when set up this way, the available shipping will depend on the customer's geographical location (determined when they REGISTER on your site).
For your purposes, you need to set your DOMESTIC (USA) shipping module to be specific ONLY to zone USA.
Then you need to install and configure ZONE SHIPPING for all other countries, by applying appropriate shipping rates for each zone. How you configure this depends a lot on what shipper you choose to work with, and the rates/regions variables that you insert into the module should be based on the rates/regions prices your shipper will charge.