Photonics-assisted millimeter-wave (MMW) wireless communications are advancing rapidly driven by the escalating congestion in the lower-band spectrum and the growing demand for higher data rates. Concurrently, Kramers-Kronig (KK) receivers provide an economical solution ideally suited for cost-sensitive deployment and application. However, the conventional KK receiver is subject to performance degradation due to the nonlinearity and memory effects introduced by practical electronic devices. In this work, the performance degradation of the conventional KK receiver is investigated and quantitatively simulated, showing that the KK receiver exhibits greater sensitivity to nonlinearity and memory effects compared to the conventional coherent receiver. To enhance the performance of KK receivers deployed in MMW communication systems, we propose a modified KK receiver employing memory polynomial compensation, namely MP-KK receiver, capable of effectively compensating memory effects whilst simultaneously addressing nonlinearity. Crucially, the memory polynomial model is employed prior to the KK algorithm to prevent further signal degradation caused by the nonlinear operator in the KK algorithm in the scenario of photonics-assisted MMW wireless communication based on the KK receiver. For verification, we present a 95 GHz W-band MMW wireless transmission demonstration with 20 Gb/s QPSK and 40 Gb/s 16-QAM signals. The experimental results indicate that the MP-KK receiver can achieve more than 3.5 dB improvement in EVM and 71.25% reduction in BER compared to the conventional approaches.