Humanoid robots operating in human-centric environments must coordinate the entire body to traverse tight, cluttered spaces while maintaining balance. Existing methods often struggle to jointly consider dynamic stability and collision avoidance from high-dimensional perceptual inputs. Moreover, for humanoids, safe behavior is inherently multimodal: the same obstacle may admit multiple valid traversals, which is difficult to represent with a single deterministic policy. To address these challenges, we propose SWAP (Steerable Whole-body Avoidance Policy), a hierarchical framework that separates collision-aware decision making from stabilization. A high-level, perception-conditioned diffusion policy generates multimodal, collision-aware motion proposals, while a low-level whole-body RL controller tracks these proposals and maintains dynamic balance. To efficiently train the high-level policy, we obtain scalable supervision via hindsight labeling: we roll out the low-level policy under randomized commands, place obstacles only in the space that each executed motion did not sweep, so the motion is collision-free by construction, and re-render the perception the robot would have seen. At deployment, Monte Carlo sampling with simple cost signals steers the diffusion model toward safe, task-aligned behaviors without heavy reward tuning. Experiments in simulation and on a real Unitree G1 humanoid show reliable avoidance with static and dynamic obstacles. Test-time steering further enables customization, improving targeted rewards (e.g., speed, orientation, or posture) by 34% on average while maintaining a high collision avoidance rate. Together, these results support a practical solution to humanoid whole-body collision avoidance with test-time steerability. Project website: https://iscoyizj.github.io/SWAP-steerable-humanoid-oa-website/

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