Are free will skeptics 'compatibilists in all but name'?

'No free will' means that we think and perceive that we make choices, but in reality these choices don't exist.

(A) Has your belief that 'there is no free will' led you to believing there are no options at all in life? That you are a puppet? If yes, this would be depressing and debilitating (that this is a real fear people have is acknowledged by Harris and other free will skeptics in their books).

(B) But on the other hand, surely you don't believe you are trapped and are an automaton. You have options, and you make choices all the time like anyone else. In this case, can you at least understand where the idea that 'hard determinists are compatibilists in all but name' (Dennett said this I think) come from?

Is (A) and (B) a false dichotomy or is this an inconsistency in the free will skeptic's worldview? Why does 'there is no free will' not imply 'we are puppets'?