Other than studying and working with their full APIs...
Is there an easy way to get the shipping zone number from FedEx and UPS if I know the "from" and "to" zip codes?
For example, is there a simple web service that I can use?
A:
Both FedEx and UPS have web-services for tracking packages and printing shipping labels etc.
FedEx provides a ready to use sample of accessing their (Tracking) web-service which probably already has the information you need.
UPS, OTOH, doesn't give you sample code, so you must read their spec and parse the xml yourself.
(At least this was true ~6 months ago, when I worked with both API's)