Have you looked at Quick Ship at all?
In theory you could use REST and BPMs to do what QuickShip does to integrate with shipping companies, but that would take a lot of time and money.
I think connecting through Worldship would be convoluted. It isn’t a modern interface, it uses flat files, and I doubt there is any REST integration. Getting the data out of epicor is easy, but then you would need to figure out how to get worldship to take the data and trigger it to send the data to UPS