Which schools of psychotherapy are most credible to a hard scientist? There is a problem in all therapies that if the client doesn't have faith or trust in the therapist then it is unlikely that anything can be achieved.  Therefore effective therapy for an extreme skeptic relies on convincing them that the therapist does indeed have some talent and ability.

Consider a profile that has something akin to the following views on common therapies:


  When looking at psychotherapy and therapists the list of different "types" seems endless.  On the one end, "Freudian" or "Psychoanalysis" is widely discredited quakery.  Carl Jung believed in "synchronicity", which puts him firmly in the quack bin.  Plenty of other therapist start talking "spirituality" and so again, sadly are filed under "not proper scientific medicine".


If someone has the above attitude to therapy and psychotherapy, what sort of therapist is going to be most credible?  We are talking about finding a credible therapy for someone who would self describe as a skeptic, atheist, scientist, etc.
For several reasons, Cognitive Behavioral Therapy (CBT) should have a good fit for someone who has a skeptic and scientific outlook on life. 


There is a large body of research showing that CBT is effective (see e.g., Hofmann et al. 2012). Obviously, this also depends on the kind of disorder. And of course, other forms of therapy can be effective too. However, for some disorders, CBT may be more effective than other therapies. For example, in a recent randomized trial, CBT was more effective in treating Bulimia Nervosa (Poulson et al., 2014) than psychoanalytic therapy (the other main form of psychotherapy). By and large, most empirical evidence we have about psychotherapy regards CBT. Despite your premise that the question is not about effectiveness, I believe that a skeptic would love that.
CBT is informed by and has inspired much basic research about the cognitive processes that may underlie different disorders. For example, there is much research about attentional processes in affective disorders (e.g., MacLeod et al., 2002). A skeptic should value this.
Another way to frame this is to say that CBT is scientific in the sense that it is based on testable theories and disorder models. In contrast many concepts in psychoanalysis, such as resistance or repression may be criticized as unfalsifiable (Popper, 1963). Again, a skeptic should prefer a more scientific therapy form.
A core technique in CBT is to question wrong beliefs and assumptions. CBT has a very rational, thought-focused way of explaining an dealing with problems (some say overly). A central tenet of CBT is that people often hold wrong (self-defeating) beliefs about the world and that they engage in schematic thought processes (e.g. someone who has social phobia may have "catastrophizing" thoughts about how others might react to him in public and therefore avoid such situations). Questioning such beliefs should be right up a skeptic's alley.
Conducting behavioral experiments to collect evidence about oneself is an important therapeutic tool in CBT (e.g., Brennet-Levy et al. 2004). Whereas psychoanalytical approaches strongly rely on the interpretation of clients' (unconscious) conflicts, CBT encourages people to collect data about their thoughts and behaviors and to conduct experiments that clarify important questions about themselves. Skeptics should love this facts-driven approach.
Whereas psychoanalytic therapies are focused on trying to solve core, unconscious intrapersonal conflicts (brought from the past) in (mostly) long therapies, CBT is problem- and behavior-focused and short. A skeptic should like this pragmatism of CBT.
Even though your question highlights the role of the therapist, this is actually not an important feature of CBT. CBT relies on structured therapeutic manuals, and not so much on talent or personality of the therapist. In fact, CBT may be effective if conducted via the internet (Andersson et al., 2009), or even in the form of self-help books (Anderson et al., 2005). A skeptic should value that CBT is focused on technique and not on the therapist.


References

Andersson, G. (2009). Using the Internet to provide cognitive behaviour therapy. Behaviour Research and Therapy, 47, 175–180. doi:10.1016/j.brat.2009.01.010

Anderson, L., Lewis, G., Araya, R., Elgie, R., Harrison, G., Proudfoot, J., et al. (2005). Self-help books for depression: how can practitioners and patients make the right choice. British Journal of General Practice, 55, 387-392.

Bennett-Levy, J., Butler, G., Fennell, M., Hackmann, A., Mueller, M., Westbrook, D., &amp; Rouf, K. (2004). Oxford Guide to Behavioural Experiments in Cognitive Therapy. Cognitive Behaviour Therapy: Science and Practice.

Hofmann, S. G., Asnaani, A., Vonk, I. J. J., Sawyer, A. T., &amp; Fang, A. (2012). The Efficacy of Cognitive Behavioral Therapy: A Review of Meta-analyses. Cognitive therapy and research, 36, 427–440. doi:10.1007/s10608-012-9476-1

MacLeod, C., Rutherford, E., Campbell, L., Ebsworthy, G., &amp; Holker, L. (2002). Selective attention and emotional vulnerability: assessing the causal basis of their association through the experimental manipulation of attentional bias. Journal of Abnormal Psychology, 111, 107–123.

Popper, K.R. (1963). Conjectures and Refutations. London: Routledge and Kegan Paul.

Poulsen, S., Lunn, S., Daniel, S. I. F., Folke, S., Mathiesen, B. B., Katznelson, H., &amp; Fairburn, C. G. (2014). A Randomized Controlled Trial of Psychoanalytic Psychotherapy or Cognitive-Behavioral Therapy for Bulimia Nervosa. American Journal of Psychiatry, 171, 109–116. doi:10.1176/appi.ajp.2013.12121511