From my own experience (I'm strictly an amateur photographer) using various point and shoot waterproof cameras, you should take their depth ratings and divide by at least 2. It's like the waterproof ratings for watches. Many don't account for the pressures of even being hit by a wave. And as Dougal mentioned - the seals are key. So every time you change the battery - you should inspect the seal (which on most point and shoots is not a simple o-ring, but a complex shaped piece of silicon. Even a piece of dust can compromise the waterproofness. You should also have o-ring grease (clear silicon grease) to keep the seals lubricated. The other problem to be aware of is having your point and shoot camera in colder water, then you come out into the warmer air/sun. Condensation between the lens groupings can be a real problem and will take hours to clear up. A housing will insulate the lens from the cool water - so condensation, if it appears, will be inside the housing and easy to wipe off - or you can use anti-fog, or put a small bag of desiccant in the housing. So IF you are serious about using your camera to a depth of 80 - 100 feet, I would recommend a dedicated housing. If it's just for one trip and you aren't going to use it regularly, then maybe it's worth the risk of just buying the Nikon.
If you don't want to break the bank - but want a very decent compact camera and compact housing - I would recommend a Sony RX100 (various versions up to V available - but would recommend minimum III and up) with an underwater housing. I have the RX100 III and the Sony housing - I use this for snorkelling as well as surfing/wave photography. It's great because even in the housing it's compact and the housing allows use of all features, including the flash. There are third party housings available too so you can pick one up for less than $400 or so. The camera will be $850 - $1400 depending upon which model (V is the latest). So you'll have a very decent underwater camera for about $1250 - $1800.