Dremil tool is high speed but low torque. You may get it to work, but if you apply much pressure, it may not work for long. I use dremil tools for everything from wood carving to polishing feed ramps to sharpening lawn mower blades; however, I understand the limitations of this small tool.
A drill motor is designed for heavier loads. Ideally you would find some way of securing the drill.
A lack of planning on your part does not necessarily constitute an emergency on my part.