Both are possible. Stylistically I prefer the first.
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brightbillyThat would have to be "captain's principles", but I don't see how this sentence could mean the same as the original.
The captains principals on safety will not compormise the safety of the crew
brightbillyWho do the principals belong to?
The captains principals on safety will not compormise the safety of the crew
It's principle, not principal.
Furthermore, principles do not have to belong to anybody.
Your sentence does not preserve the meaning of Anonymous's sentence. Anonymous's sentence makes it clear that the captain is not