In that case look for a wind-up or self-wind watch from the 60's or marked as a "chronograph". The Rolex Oyster comes to mind if you're willing to spend the bucks, but there are less expensive to be had if you search. You might find an old Citizen or other brand but the new ones are likely to be digital. Then again, as SG pointed out the digital watches are much more accurate and by the time your battery ran out your mechanical watch would have drifted enough to be somewhat useless for navigation.

If you're thinking of your boat as a survivalist strategy, that's a pretty deep subject. If that's a concern the first thing to do is think about changing your life so you live and work far from a major target.