Stigma has emerged as one of the major obstacles to effectively diagnosing depression, as it prevents users from open conversations about their struggles. This requires advanced questioning skills to carefully probe the presence of specific symptoms in an unobtrusive manner. While recent efforts have been made on depression-diagnosis-oriented dialogue systems, they largely ignore this problem, ultimately hampering their practical utility. To this end, we propose a novel and effective method, UPSD$^{4}$, developing a series of strategies to promote a sense of unobtrusiveness within the dialogue system and assessing depression disorder by probing symptoms. We experimentally show that UPSD$^{4}$ demonstrates a significant improvement over current baselines, including unobtrusiveness evaluation of dialogue content and diagnostic accuracy. We believe our work contributes to developing more accessible and user-friendly tools for addressing the widespread need for depression diagnosis.