rent a car from Cartagena Cruise terminal

OUr itinerary is 2 nights in Cartagena first. A one week South Caribbean cruise afterwards. And 3 last nights until we come back.

For those 3 days - nights we are planning to go to Santa Marta and Tayrona National park. 2nd night at Tayrona. Last night at Santa Marta. Our flight departs around 7:00 pm.

A question: is it possible to pick up the car at the Cruise terminal and drop it off at the Cartagena Airport? Or it would be easier to take a taxi or transfer to the Airport and pick it up there? Do you know some rental cars company which works at th terminal cruise and Airport too?

Thanks in advance!