The emerging paradigm of 6G multiple Radio Access Technology (multi-RAT) networks, where cellular and Wireless Fidelity (WiFi) transmitters coexist, requires reliable mobility decisions under fast channel dynamics. Handover in multi-RAT deployments is still reactive, relying on instantaneous measurements and threshold events. This work proposes a Machine Learning (ML)-assisted Predictive Conditional Handover (PCHO) framework based on short-horizon signal quality forecasts. We present a generalized P-CHO sequence workflow orchestrated by a RAT Steering Controller, which standardizes data collection, parallel per-RAT predictions, hysteresis-enabled conditions, and CHO execution. Considering a realistic multi-RAT environment, we train RAT-aware Long Short Term Memory (LSTM) networks to forecast the signal quality indicators of mobile users along randomized trajectories. The proposed models are trained and evaluated under 6G and IEEE 802.11 WiFi integrated coverage. We study the impact of hyperparameter tuning of LSTM models under different settings, and compare direct multi-step versus recursive P-CHO. Comparisons against baseline predictors are also carried out. Finally, the proposed P-CHO is tested under soft and hard handover settings, showing that hysteresis-enabled P-CHO scheme reduces handover by 40%, eliminating pingpong events. Overall, the proposed P-CHO framework can enable accurate, low-latency, and proactive handovers suitable for ML-assisted handover steering in 6G multi-RAT deployments.