I would go with the second example, though it is hard to say technically without more medical details (possibly either could be OK).
As a language matter, I think you need to think of this in two parts.
First, transfer implies a short term/distance movement from A to B. transport indicates more time or distance is involved.
Oxygen from the lungs transfers to the red blood cells.
The flow of blood transports oxygen from the lungs to the brain.
For another example, let's say you sending freight from Seattle to San Francisco, and it changes trucks in Portland. Then you could say:
The shipment will transfer between trucks A and B in Portland.
The company C will transport the shipment from Seattle to San Francisco.
You could use this example with people, though you would probably use travel instead of transport.
We will travel from Seattle to San Francisco. We will transfer between train A and train B in Portland.