To get a decent photo on PotC, you pretty much require a DSLR with a very fast lens - one that doesn't zoom at all. Point-n-shoots have a very small imaging sensor, which allows the camera to be small but it also means trouble when the camera is trying to squeeze a lot of megapixels out of it and be sensitive for low-light shooting.
There's three parts to a camera's settings - shutter speed, aperture (aka F-stop), and sensitivity (aka ISO). To get a decent photo on a moving ride like PotC, you need a reasonably fast shutter speed. To get that, you need a "faster" aperture and high sensitivity. PnS cameras are limited to whatever aperture the camera lens was built with - if you're lucky, you might have F2.8 when not zoomed in. I think you'll need at least F1.8 or less to get decent results. In addition, you'll generally need sensitivity levels of at least 1600 - most PnS cameras show serious noise at only ISO 400, and ISO 1600 is either unavailable or extremely noisy.
IaSW is slightly brighter so you
might be able to get away with a point-n-shoot, set your camera for the highest ISO level, set the shutter speed to 1/60th or 1/90th or so, zoom out as far as possible, and take a bunch of pictures.
And thanks for not using a flash, it's definitely appreciated by everyone else with you on the ride.
If you want to be really super-considerate, you can also not use the LCD screen at all, use the viewfinder to compose the shot and turn off the post-shot review.
Good luck!