Actually the most dangerous US branch of service in terms of lethality was a pretty forgotten one, the United States Maritime Service or USMS for short. With an overall lethality of 4,5% over the course of WW2 they have both Army and Marine Corps beat (with 3,3 and 3,7% respectively). Back to your question, your odds of surviving WW2 aboard a Navy Vessel are 98,5%. Your odds of surviving without so much as a scratch on you are 97,6%. Of all the major branches of service it was by far the "safest" one.

That said, the Navy had the lowest proportion of wounded relative to dead of any branch which is largely explained by a few factors. Namely that naval gunnery and aviation used very heavy weaponry. Your odds of being wounded rather than killed are simply better if you're hit with a rifle or shrapnel than if you're caught in the blast the main armament of a battleship. The second factor is that if you're wounded, land is a much better place to be than floating in the north atlantic with not a ship in sight. The relatively catastrophic nature of a warship sinking is also a rather bad environment. A giant steel tub filled to the gunwales with explosives and fuel has a rather unfortunate tendency to explode and sink quickly which makes escape difficult.

You can find all the statistics for this in the reports Battle casualties by type of casualty and disposition, type of personnel, and theater: 7 December 1941 – 31 December 1946 volume 1-7. They're available through the Combined Arms Research Library.