Then I switch to producing worker. Once the boat gets to the fish combined with with size 2 city production time is something like 8-9 turns. But midway through worker production I get BW, switch to slavery and whip my worker finished.
That's around T22-23, correct? So we're essentially comparing a Fishing-BW, warrior-workboat-worker opening to a BW-Fishing, worker-warrior-workboat opening that ends almost on the same turn (@Gumboat said 20 earlier but I doubt BW-Fishing can be researched before T22 on immortal.) Main difference is in your opening the warrior is out earlier and the boat is out earlier (so you get that extra food and commerce) vs. in @Gumboat's the worker is out earlier and build a mine and chop one more forest (extra production, so maybe the next boats come out a bit faster). Again it's a bit tedious to try to simulate it on paper beyond the early turns.
Are you playing Gandhi or Ashoka? With Gandhi (Philosophical), getting Writing earlier has a greater appeal since a library with two scientists working it produces a great scientist in 9 turns only. With Ashoka, you get cheaper lighthouses so perhaps Sailing gets more value, you could even go for the Great Lighthouse with such a water-dominated start, in that case you probably delay AH-Writing even further. However it really depends on what the map looks like, where the cities are planned, etc. Why would you want iron working early?
When should you produce a second city by?
Fippy's beginner guide suggests growing the city to work all the "good tiles" before producing a settler, and it's generally good advice. At that point either you produce it without whipping which stops growth, or you let the city grow further and whip to take the population down, but ideally big enough to still work good tiles. With just fishing and mining, you best tiles are the 3 boats and the pig mine, and working them all at a population of 4 you get a settler in 8 turns. But alternatively, you can let it grow to 6, at which point it's unhappy, get 10 production into the settler and whip to finish the settler, dropping the population to 3 (but you need to grow back to 4 to get all your good tiles). The advantage of the second option is that you can put production into something else while it's growing. If you have a granary (but that requires pottery) whipping becomes much better, but before a granary, often just stopping growth with all the good tiles worked is best.
Obviously if you go for Hunting-AH next then the pasture pigs become the best tile for growth and settler production, but you have so many good tiles you may not need to wait for / prioritize that, unless it fits in your bigger plan.
A good benchmark that people use is to have 3 cities by turn 50 (the capital might go settler-worker-settler for example).
Note that if your 2nd city is also on the coast and all the coast tiles between it and your capital are within your borders, then it's connected by trade even without sailing.