Depends; Do you have to carry a heavy wooden cross after?
Nah, this idea of carrying a wooden cross is a misconception. Most people about to be crucified probably walked from the jail to the execution site with a beam with their arms tied to it and once their reached the site, the soldiers hammered the nail through his wrists, lift the guy, place the beam unto the piece already planted on the ground, hammer the nails in the feet and wait for the person crucified to slowly get out of breath from having the arms extended upward, making it harder to breathe.
Since Crucifixion was the Roman's favorite way of dealing with people condemned to die, it'll make sense to already have the site prepared so they could do their job efficiently.
