Did the Cook know the original mission orders?
Young Mr Putin there, he had such a career ahead of him, said he did not know who was on-board. Maybe he did, maybe he didn't, but he didn't know the mission orders until he read them out in Ramius's cabin.
Perhaps the Cook knew what they were supposed to be doing, heading North for search / evade testing etc?
Having seen the "accidental" death of Putin and the announcement that they were to sail to the US coast, conduct tests then on to Cuba, might have been his trigger to sabotage the boat.
"..listen to their rock and roll" Get with the times Ramius, it would be Grunge and Hip-hop by then.