SW, S or SE are obviously the winds that chop up more than the land based ones. 13-15 knots would likely be a F4 - so in a 16' boat with a southerly wind, it would be bordlerline depending on experiance and the actual size of the boat (16' boats vary hugely!)
If you stay close to the shoreline (up to 1 mile out) you can fish Christchurch in pretty strong winds as the land affords protection. Ive fished off the beach huts in a NW 6-7 and it was fine.... it's a tough call though, and even a decent looking forcast on the web can be very different when you get out. Tides, air pressure and previous weather all effect conditions.
As for the fog - dont panic - make sure youve got a compass, and take a bearing incase the GPS fails. Make sure you have a foghorn onboard incase you hear engines close by, and keep a damn good look-out.