cockerel or mange?

[NatJ]

No sign of parasites but I dusted it with permethrin just in case.

Sounds good

Could it be a frizzle?

I don't think so. Frizzled feathers usually stick out a bit differently than that.

Here are two threads that have photos of frizzles (first post of each thread):
https://www.backyardchickens.com/threads/frizzle-roo-or-hen.778518/
https://www.backyardchickens.com/threads/12-13-weeks-old-boy-or-girl-frizzle.908242/