It's no problem to have a different origin for your shipments than the return address that's printed on the label.
Just head to Settings > Ship From Address to edit or add a new ship from address, and uncheck the checkbox at the bottom:
The Physical Address is the "Origin," and is where the postage rates are calculated from. You have to enter a full address for the Physical Address of where your shipments will originate, not just the zipcode.
For example, you could enter the address of the Post Office you'll be dropping off at (use the USPS Post Office Locator to find the address).