To preserve or not to preserve prosody is a central question in voice anonymization. Prosody conveys meaning and affect, yet is tightly coupled with speaker identity. Existing methods either discard prosody for privacy or lack a principled mechanism to control the utility-privacy trade-off, operating at fixed design points. We propose DiffAnon, a diffusion-based anonymization method with classifier-free guidance (CFG) that provides explicit, continuous inference-time control over prosody preservation. DiffAnon refines acoustic detail over semantic embeddings of an RVQ codec, enabling smooth interpolation between anonymization strength and prosodic fidelity within a single model. To the best of our knowledge, it is the first voice anonymization framework to provide structured, interpolatable inference-time prosody control. Experiments demonstrate structured trade-off behavior, achieving strong utility while maintaining competitive privacy across controllable operating points.