While sighted users leverage both keyboard and mouse input devices to interact with desktops, non-visual users, i.e., users who are blind, cannot use a mouse as it only provides feedback through a visual cursor. As a result, these users rely on keyboard-only interaction, which is often cumbersome, inefficient, and error-prone. Prior work has shown that using a small, rotary input device benefits blind users significantly, as it simulates mouse-like operations. In this paper, we extend this prior work by proposing Wheeler, a multi-wheel based input device that provides simultaneous access to UI elements at three different hierarchies, to facilitate rapid navigation and mouse-like interaction. We designed Wheeler from scratch in multiple iterations and assembled it using 3D printed models and commercially available electronics. A preliminary user study with six blind-folded sighted users revealed its potential to become an essential input device for blind users, as well as a training and learning tool.