You seem to imply that wisdom is in direct contradiction with rationality, and so should be discarded. If being wise is primarily focused on being unbiased and impartial then this holds, but focusing on how you appear doesn't seem particularly like wisdom. Caring about whether one appeared wise or not automatically precludes someone from being wise, and puts them directly into the "pretending to be wise" camp. But true wisdom, using all the tools available to you to solve a problem, seems to be in harmony with rationality, not opposed to it.