The follwing tip will save you a lot of cleaning time and hassle. Before drilling holes (or making any other similar dirt-making tasks), cover the surface underneath with damp kitchen towels. In the picture above, I covered the top of my cooker, making sure the damp sticky paper towel bridged the gap between wall and cooker. When you have finished drilling, simply remove the paper towel gently and throw out.
Be careful with water-sensitive areas though such as wood. To use this method still and not spoil the surface, you could place a plastic sheet underneath the paper towel.