Ummm... Jacobson v. Massachusetts, 197 U.S. 11 (1905) kinda tanks the theory re no coercion tbh.

Plus, I don't believe prep itself states that the vaccination must be voluntary. If it does, which specific subsection?
https://www.law.cornell.edu/uscode/text/42/247d-6d

I think the big issue is that the statute prohibit judicial review of the secretaries decision, which means that the secretary doesn't have to follow prep at all, other than issuing a declaration, because no court can review it. That's a problem, because there is no protection where the secretary exercises his discretion maliciously or in violation of law. This is beyond chevron deference.