We just finished Plunder and Peril, and it was great fun. We liked it better than Raiders of the Fever Sea, which is the second part of Skull and Shackles. I think you'll want to keep Tempest Rising because it has a lot of cool elements and important plot points.
Plunder and Peril has many NPCs to interact with and if PCs play their cards right, by the end of it they might
I'm currently GMing Skull & Shackles, with my group right at the end of book 3. I have also GM'd the first two chapters of Plunder & Peril (co-GMing with my wife, for a different group) and will be finishing the third soon.
I think, for deciding whether or not to substitute Plunder & Peril for Book 2, it really comes down to whether or not your players are excited about Ship Combat and the rules for executing ship to ship battles.
If they are more focused on their group of characters and enjoy that aspect more, or do not have much/any interest in ship combat and its accompanying rules, then Plunder & Peril can be a great substitute.
I would be hesitant to do a "super" chapter 2 by combining both, as I think you run the risk of your player's gear and/or wealth getting a bit out of hand.
I combined both of them in a way as I felt that P&P had a better plot and flow than the AP did. Running them as is though, the biggest difference would be that the module does not have the PCs in their own ship while Fever does.
I used a physical split treasure map instead of Inkskin's tattoo and the 3 reasons to live and introduced Varossa to the PCs so they could ally together to chase the treasure. I replaced the final destination with Bonjo Tombo from Dead Man's Chest.
They're really only overlapping in the respect that they run the same levels. I agree that if your PCs don't care about ship-to-ship combat or actively dislike it, "Plunder & Peril" is more of a possibility. But if they don't like that, you can also just cut it out of "Raiders" and run it fine.
On the flip side, "Wormwood Mutiny" goes the whole book with giving very little player agency. One of the book's biggest pay-offs is ending with your own ship and all the agency you'd want. Replacing "Raiders" with "Plunder" means you're basically removing that agency as soon as the players get it and subordinating them to another captain all over again.
Do you think your players are likely to park their ship in Lilywhite and then immediately join a contest to join another captain's crew? What happens to the crew of their newly-won ship? Do they just hangout in town while the PCs take on this new adventure? Do they also join the crew of the Magpie Prince and does doing so change the balance of power on that ship? Those are some questions to consider.
I'm a proponent of "Raiders" and keeping it in the campaign.
So far (and I haven't read all of Plunder yet), I was thinking of running Raiders up to the fight with the Ghost ship, then having their ship so damaged that they have to take it to Lilywhite for repairs (maybe with a storm or one of the nastier ship-to-ship combats).
While it's being repaired, the PCs could do the first two modules of Plunder.
Ideally then they could take the rock and then do the last parts of both modules one after the other.
I'm still reading it all, though, so I'm not sure about interweaving the 5th level and 6th level parts of both modules.
You could always start with Souls for Smuggler's Shiv then use Plunder and Peril then jump into the actual Skull and Shackles with Tempest Rising :-)
I actually find this solution more workable than going form "Wormwood" to "Plunder". Simply run "Souls for Smuggler's Shiv" as is and have the Magpie Prince be the ship that rescues the PCs in the end. Cut out the contest to join the crew at the beginning of "Plunder" and simply have the captain press them into service in return for their rescue.
This works fine if you expect this to be a two module campaign. If you think that you'll then start running "Tempest Rising" after "Plunder & Peril", you'll have a lot of work to do because Barnabas Harrigan is a major enemy from "Tempest" through "The Price of Infamy" and he's going to basically come out of nowhere in the Free Captain's Regatta. While I guess you could say his campaign of vengeance is because he lost the race, it won't be nearly as satisfying or believable without "Wormwood".