Meta-Reinforcement Learning (Meta-RL) agents can struggle to operate across tasks with varying environmental features that require different optimal skills (i.e., different modes of behaviours). Using context encoders based on contrastive learning to enhance the generalisability of Meta-RL agents is now widely studied but faces challenges such as the requirement for a large sample size, also referred to as the $\log$-$K$ curse. To improve RL generalisation to different tasks, we first introduce Skill-aware Mutual Information (SaMI), an optimisation objective that aids in distinguishing context embeddings according to skills, thereby equipping RL agents with the ability to identify and execute different skills across tasks. We then propose Skill-aware Noise Contrastive Estimation (SaNCE), a $K$-sample estimator used to optimise the SaMI objective. We provide a framework for equipping an RL agent with SaNCE in practice and conduct experimental validation on modified MuJoCo and Panda-gym benchmarks. We empirically find that RL agents that learn by maximising SaMI achieve substantially improved zero-shot generalisation to unseen tasks. Additionally, the context encoder equipped with SaNCE demonstrates greater robustness to reductions in the number of available samples, thus possessing the potential to overcome the $\log$-$K$ curse.