Do we need the +1 Fur
for those 4 turns? Could you send the promoted Phalanx elsewhere? Is a LH better than an earlier, unpromoted Catapult? If you think so, then ok.
As you noticed, Whale city will be unhappy @T113 without the Fur. Actually I'd probably send at least a Phalanx+Spear to the Horse site for defense as Shaka's SOD is going to move there. We are lacking catas to start the war so we could spare some units there.
If we must work an unimproved Fish for one turn, the loss is either 3H (build Worker) or 3F (build Granary).
Building a Worker, the improved city generates 6HPT. Growing, the improved city generates 5FPT and 1HPT.
5F * 5 = 25/22F
After the whip, 3F remain.
5F * 4 = 23/22F
So building a Worker immediately gains +3F and saves a turn of growth. The ultimate difference is +2F 3H +3C.
If you build Culture with a Worker queued, the gain is +5F, which will save a second turn of growth.
Not true, the culture bug only works 1 turn when the border pops, so it's basically just a gain of 1 culture and 1H to granary in the same time. We can't build Culture with a Worker queued @T5, otherwise the city will grow to size 2 while the hammers to worker is not enough.
Overall difference from both actions would be +7F +6C 4H, I suppose, which means whipping a Lighthouse 12 turns sooner for another +2/+4F and more commerce, etc.
My intuition is that starting a worker immediately will be slightly better, but won't be that much. I usually will just take other's thought when I feel right and don't bother to test further.
I've been thinking about whether we should send one Settler towards The Hague, if there is not a suitable candidate to produce a Settler for Deer/Cow/Gems.
The site is not good during the war as we need to put defense there. Shaka's units could attack the site from 3 cities. Moreover, we don't have workers ready to improve or unsafe while 3 workers in that areas are busy at chopping and roading.
If Shaka doesn't target a barb city, I don't know if we could use a temporary gift city to Willem to move Shaka's stack. I don't think we can, which is why I didn't suggest it before.