Start off by getting fish and cider production going, and head off to the beggar's island (central on the map, NW of the Corsair's Lair). The quest there asks for fish and cider and gives you a +10% speed sail which you need. Get this, put it in your flagship (make sure there's no other goods in your flagship which will slow it down), save the game (in case it goes wrong!) and start the first race.
The key with the race strategy is that you can't beat the other ships on speed on the straights, but you can pass them in the corners (at the waypoints)! The other ships will sail to each harbour waypoint and stop for a few moments before setting off again. You, on the other hand, need to be watching and ready, and as soon as you get near to the waypoint you will be told of the next waypoint - click on this on the minimap as soon as it appears and you can 'cut the corner' and hence save a significant amount of time.
There are certain other things that you can use to help - if you do the race more than once, you know where the waypoints are and so you can anticipate the turn, making sure you sail to the right side of the waypoint so you can turn quicker. Also, there are some places where the 'auto-routing' for the ship will take you round a pair of islands, whereas with a bit of careful manual steering you can go between them - you'll work these out quickly enough.
Once race 1 is over - straightforward with the extra sails - you need to find Guy Forcas (North-East of the map) and do his quest (sink 3 ships, reward is a white flag).
Somewhere along the way here you need to get stone, expand your city to 355 citizens, then build a repair crane. Tools are probably worth setting up as well though you could possibly get away with buying what's needed.
Now for Race 2 and 3. The problem you'll get on race 2 is watchtowers on islands that you pass which will fire on you, hence the white flag. However, the key to my strategy is that you have the flag on the ship but don't activate it until you are nearly at the islands, ie just after you've passed the second waypoint. Using the corner-cutting technique you should win this race without too many problems, and more importantly should still have several minutes of life left in your white flag.
Now the clever bit. When you win this race, save the game then immediately start race 3. In race 3 your threats are a thunderstorm and several enemy ships which will fire on you and all the other competitors! Your white flag should still have several minutes left on it, so if you go straight into race 3 your flagship will get damaged by the thunderstorm, but you will get past all the enemy ships before the flag runs out and not get fired on whereas all your competitors will get attacked. As a result, you should come out less damaged than the other competitors and therefore ahead of them - if they survive at all!
For race 4 you are taking on the corsair's fastest ship. You cannot beat this ship in a straight race with your flagship but you can outwit him. The race goes along the shore of the long island in the east of the map. Get a second ship (I used 50 honour to buy a scroll and took them to Al Zahir and got the ship from him - you could also buy a ship from the corsairs), and repair your flagship. Build a warehouse on one end of the island and a harbourmaster's office at the other end, position one of your ships at the far end, take the other ship to the corsair's lair and run the race in two legs - sail the treasure to the island and unload it then immediately load it onto the other ship and sail it to the finish.
It's fortunate that there isn't an achievement of winning all the scenarios and all the quests (as there was in base 1404) since you don't do half the quests with this approach, however it does reward careful control of your ship and therefore is great fun. If you've already done the scenario by conventional means, give it a try!