London for a 5 year year old who loves Pirates and old ships.

Cross-posting from r/UKTravel in hopes of more local recommendations. Since it became a slight distraction in the other post, I’ll clarify that “trip of a lifetime” is intended as hyperbole…

I am planning the trip of a lifetime for my small child who loves pirates and old ships. He’ll have just turned 5 when we travel to London (from California) for 10 days in late June. My own interests are architecture and design so a bit of that doesn’t hurt either.

We’re staying the first half near Hyde Park, and second half near Tower Bridge, so will have the Uber boat at our doorstep.

So far I have:
- Diana memorial playground, if open
- Serpentine lake boating & Serpentine Pavilion
- Uber Boat to Greenwich for Cutty Sark and Maritime Museum
- Golden Hinde
- Sword fighting demonstration at the Globe
- Tower of London for Crown Jewels and armory
- Uber boat to Battersea Power Station & Park
- We will likely visit the Science & Natural History museums as well.

Questions:
- Any other ideas for relevant things to do and see?
- Food - Maybe Peter Pan Tea? The menu looks a little challenging for my child. Where to eat instead that is on theme and has simple child-friendly food on the menu? He’s well behaved in restaurants but not an adventurous eater.
- Special pirate child request - is there anywhere with quality child sized tricorn hats, or custom hats under £300? I made the last one several years ago (modified and decorated a store bought felt hat) and he has outgrown it. It would be special to pick one up in London from a proper hatter or milliner. I know this is a bit over the top but it is his prized possession.