ISAC systems introduce new privacy risks because an unintended sensing node may exploit the shared radio waveform to infer transmitter-related information even when the communication payload remains secure. This paper investigates transmitter privacy, defined as limiting unauthorized inference of transmitter-related information through channel estimation, in a RIS-aided multi-antenna wireless system with a transmitter, a legitimate receiver, a malicious sensor, and a RIS. The malicious sensor is assumed to estimate the transmitter--sensor channel, and the resulting channel state information can then support unauthorized sensing, inference, or related signal processing. To mitigate this threat, we consider a privacy-oriented design in which the transmitter adopts superposition-based signaling with a message signal and transmit-side artificial noise, while the RIS shapes the propagation environment in a privacy-aware manner. The channel-estimation performance at the malicious sensor is first analyzed under imperfect prior knowledge, and both the true and predicted mean-square-error expressions are derived. Based on this analysis, we formulate a joint active--passive beamforming design problem that maximizes the malicious sensor's predicted channel-estimation error subject to a communication quality-of-service constraint, a transmit-power budget, and the unit-modulus constraints of the RIS. The resulting non-convex problem is handled through a numerically efficient alternating-optimization framework based on an augmented Lagrangian reformulation. Numerical results show that RIS-assisted propagation shaping can substantially degrade unauthorized channel estimation relative to the non-RIS case while preserving reliable communication, and further show that the privacy gains also improve a more direct sensing metric, namely the malicious sensor's angle-of-arrival estimation accuracy.