For robots to successfully transition from lab settings to everyday environments, they must begin to reason about the risks associated with their actions and make informed, risk-aware decisions. This is particularly true for robots performing mobile manipulation tasks, which involve both interacting with and navigating within dynamic, unstructured spaces. However, existing whole-body controllers for mobile manipulators typically lack explicit mechanisms for risk-sensitive decision-making under uncertainty. To our knowledge, we are the first to (i) learn risk-aware visuomotor policies for mobile manipulation conditioned on egocentric depth observations with runtime-adjustable risk sensitivity, and (ii) show risk-aware behaviours can be transferred through Imitation Learning (IL) to a visuomotor policy conditioned on egocentric depth observations. Our method achieves this by first training a privileged teacher policy using Distributional Reinforcement Learning (DRL), with a risk-neutral distributional critic. Distortion risk-metrics are then applied to the critic's predicted return distribution to calculate risk-adjusted advantage estimates used in policy updates to achieve a range of risk-aware behaviours. We then distil teacher policies with IL to obtain risk-aware student policies conditioned on egocentric depth observations. We perform extensive evaluations demonstrating that our trained visuomotor policies exhibit risk-aware behaviour (specifically achieving better worst-case performance) while performing reactive whole-body motions in unmapped environments, leveraging live depth observations for perception.