This study investigates the safety of powered two-wheelers (PTWs) during “on the fly” and “oblique maneuver”-type overtaking behaviors in urban mixed and weak-lane-disciplined traffic using the proactive approach. A two-dimensional conflict indicator, Anticipated Collision Time (ACT), was employed to detect conflicts involving PTWs during overtaking. The crash risk for each type of PTW overtaking maneuver was then estimated using the extreme value theory (EVT) approach. The study findings reveal that PTWs predominantly perform “on the fly” overtaking maneuvers compared to “oblique maneuver”-type overtaking and show a preference for left-side overtaking in urban traffic, although right-side overtaking also occurs frequently. PTWs maintain smaller lateral gaps when overtaking from the right side compared to the left, regardless of the overtaking maneuver type. Importantly, the crash risk associated with “oblique maneuver”-type overtaking was found to be more than twice that of “on the fly” maneuvers. These findings highlight the need for targeted safety measures to mitigate the increased crash risk associated with specific overtaking maneuvers and lateral gap management. Public awareness campaigns can further educate PTW riders about high-risk overtaking maneuvers and promote safer riding practices.