Modern LLM agents increasingly rely on skill libraries to handle complex tasks, making skill evolution a primary driver of self-improvement. However, isolated single-user task streams lack the diversity required to build comprehensive skills. While cross-user collaboration can overcome this data bottleneck, current trajectory-sharing approaches compromise user privacy and impose a uniform global library that fails to accommodate client heterogeneity. We introduce FederatedSkill, a privacy-preserving framework for collaborative agent evolution. Moving beyond raw trajectory sharing, FederatedSkill utilizes semantic skill diffs, structured patches over local libraries, as the fundamental unit of communication. On the server side, an evolution agent aggregates these patches to dynamically model client-specific capability boundaries, facilitating strictly personalized skill evolution rather than a suboptimal global average. Evaluated across 20 distinct agent task families, FederatedSkill demonstrates substantial gains over self-evolving baselines, achieving up to a 44.4% increase in success rate and a 37.5% reduction in computational cost.