Apart from very specific points on a human (such as the jugular) most major veins (arteries) are deep inside the body out of harms way [...]
As will they be on a spaceship. Animal skin is "dead"; we don't have living cells that need to be supplied with blood all over the surface of our bodies. In the same way, an organic spaceship would be surrounded by a crystalline structure of dead organic cells, forming armor. Or even better, inorganic armor and an organic interior.
An interesting question that never comes up is power generation. Does an organic ship carry the standard SciFi fusion/fission reactor, or something else? Also, how would an organic ship propel itself?
Someone else touched on this earlier. Standard biological metabolism methods won't generate nearly enough power for beamz and engines.