I'm not entirely sure I understand what your concerns are. This is how I see it:
OPTION A: Write book and risk revealing secrets that might be used by potential competitors + be seen as a "designer" rather than a "unicorn".
OPTION B: Don't write book and focus on applying the principles of it on your startup.
Have you considered doing this instead:
OPTION C: Apply principles of the book to the startup and document it via a blog as you go along. After startup is launched and you've met your success criteria, you'd have amassed a collection of short posts, with--hopefully--some success/lessons learned to back them up, not to mention an audience of people who are captivated by your progress. Then, collect all your blog posts, bind them together, scrub, and sell to said audience.
You'll only know whether your lessons and skills are revolutionary if you can put them to the test. Even better if you can take people along the ride with you. You don't have to reveal any sensitive IP or technological solutions - but people appreciate transparency and generosity.
Not to mention, if your competitors could use your own lessons and use them to deliver better products than yourself, then perhaps your ideas weren't meant to be exclusive to you in the first place?