(How) can you teach a subject effectively for which you are a skeptic without biasing students?
What "skepticism" means to an academic is strongly field-dependent.  I am a mathematician, and I would have thought that true skepticism is almost impossible: after all, mathematical results are proved and any standard course would be on things that have been proved, reproved and combed over by the community several times over.  I could however be skeptical of the future trajectory of a mathematical subfield: i.e., maybe I think it is not worth the students' time to learn it.  But this is just a way of saying that I have very little interest in that subject, so...why then would I teach it?  I suppose that's one of the luxuries I have as a tenured faculty member in a reasonably large department.

So I looked at your profile, and I am interested to see that your field is...statistics.  So, hmm: again I wonder what you mean by "skepticism."  Do you mean that the course concerns a statistical technique that is mathematically valid 
but whose usefulness is vastly overstated or is typically applied outside its range of validity, or a statistical practice that is actually not grounded well in theory, or...what?  I would think that "belief" has little to do with statistics, but perhaps that is a naive pure mathematician's belief.

On the face of it, if the course is in subject X, then spending some of the course covering X, then in the middle revealing that you don't believe in X, then spending the remaining portion of the course having the students decide which is right sounds, well, weird.  It is liable to leave them wondering why they took the course at all.  Indeed: why is this course being given? You said that there was one "believer" faculty member who is no longer in the department, so...who wants the course now?  Inertia is not a great defense for an academic position.  As a new tenure track professor in your department, in theory you should have some say in the programmatic offerings and also some responsibility.  In practice, the responsibility lies much more with senior people than very junior people.  I recommend that you contact faculty mentors and discuss your concerns with them in a mild way, making clear that you will do what they think is best.  One idea is to propose replacing the course with a totally different course in a subject close to your own expertise and enthusiasm: other things being equal, that sounds like a much better course.  If however the department is really committed to the course: well, you said you would do it, so I would suggest that you really do it, and not include skepticism of X as a main part of the course.  You can rest easier at night knowing that you offered the department some alternatives.  Speaking as someone who currently has an administrative role in my department: believe me, I am painfully aware that on a wide range of topics, "the buck stops with me."  That is my problem; as someone who has not even started the tenure track job, it is not yet yours.