When operating at their full capacity, quadrupedal robots can produce loud footstep noise, which can be disruptive in human-centered environments like homes, offices, and hospitals. As a result, balancing locomotion performance with noise constraints is crucial for the successful real-world deployment of quadrupedal robots. However, achieving adaptive noise control is challenging due to (a) the trade-off between agility and noise minimization, (b) the need for generalization across diverse deployment conditions, and (c) the difficulty of effectively adjusting policies based on noise requirements. We propose QuietPaw, a framework incorporating our Conditional Noise-Constrained Policy (CNCP), a constrained learning-based algorithm that enables flexible, noise-aware locomotion by conditioning policy behavior on noise-reduction levels. We leverage value representation decomposition in the critics, disentangling state representations from condition-dependent representations and this allows a single versatile policy to generalize across noise levels without retraining while improving the Pareto trade-off between agility and noise reduction. We validate our approach in simulation and the real world, demonstrating that CNCP can effectively balance locomotion performance and noise constraints, achieving continuously adjustable noise reduction.