Given the potential of solar sails for applications around Earth, this paper investigates their performance in executing collision avoidance maneuvers. An extensive set of conjunctions (e.g., varying orbital regimes, sail control authorities, and collision geometries) is built. An "ideal" and a "real" case are examined, with the latter accounting for greater uncertainties (modeled via a covariance-mapping algorithm) and stricter collision probability requirements. The optimal control problem is derived and solved through direct collocation, seeking time optimality while constraining the probability. For all scenarios, maneuvers are completed within the one-day threshold, proving solar sails fit the current operational framework. Key findings are: 1) Better debris state knowledge (and later warnings) reduce maneuver time; 2) Higher altitudes increase the maneuver time, while greater sail control authority decreases it; 3) Eclipses influence results; 4) The Earth-Sun configuration only weakly affects the maneuver time; and 5) In-plane control is always non-zero. The locally optimal steering laws to change the semi-major axis and eccentricity best approximate the optimized maneuvers: especially for longer maneuver times, these straightforward laws comply with collision probability requirements.