In defense of the opening scene, it is the best scene in the film, it's the one scene that makes the most cinematic and narrative sense, it's beautiful and unique to this film.

So that poses a problem if you want to move it... where?

It has to be the opening scene.

Now some may say it reveals the Jockey's true form too soon but if you remove the surplus to requirements head revival scene the only time we know for sure that the baldies are the elephant trunk guys wearing a skull helmet is when the chair powers up.

Why an archaeologist would want to contaminate a site and the ship by bringing back a biological sample makes no sense.

I could see her bagging a tablet or an object (like an urn, if she didn't know it's contents or it appeared empty) but surely a decapitated head would be something an unethical biologist might have sneaked in.

It makes Shaw seem to be similar to David who in total disregard to the safety of his Creator (he might not like him but his hotwired to obey him) brings back the urn and tests it on Holloway but seeing as we are not meant to have the same relationship between these characters it could be removed but then you would have to also trim the storm scene (either giving her something else to go back for or cut that cliched aspect of the scene altogether).