In this paper, we consider a challenging secure wireless sensing scenario where a legitimate radar station (LRS) intends to detect a target at unknown location in the presence of an unauthorized radar station (URS). We aim to enhance the sensing performance of the LRS and in the meanwhile prevent the detection of the same target by the URS. Under this setup, conventional stealth-based approaches such as wrapping the target with electromagnetic wave absorbing materials are not applicable, since they will disable the target detection by not only the URS, but the LRS as well. To tackle this challenge, we propose in this paper a new target-mounted IRS approach, where intelligent reflecting surface (IRS) is mounted on the outer/echo surface of the target and by tuning the IRS reflection, the strength of its reflected radar signal in any angle of departure (AoD) can be adjusted based on the signal's angle of arrival (AoA), thereby enhancing/suppressing the signal power towards the LRS/URS, respectively. To this end, we propose a practical protocol for the target-mounted IRS to estimate the LRS/URS channel and waveform parameters based on its sensed signals and control the IRS reflection for/against the LRS/URS accordingly. Specifically, we formulate new optimization problems to design the reflecting phase shifts at IRS for maximizing the received signal power at the LRS while keeping that at the URS below a certain level, for both the cases of short-term and long-term IRS operations with different dynamic reflection capabilities. To solve these non-convex problems, we apply the penalty dual decomposition method to obtain high-quality suboptimal solutions for them efficiently. Finally, simulation results are presented that verify the effectiveness of the proposed protocol and algorithms for the target-mounted IRS to achieve secure wireless sensing, as compared with various benchmark schemes.