I did exactly the same way. The problem was the screwdrivers from the link were a bit small and delicate.
JIS-compatible screwdrivers are available in all imaginable configurations: Longer, shorter, thin or thick handle, thin or thicker shaft, etc. Thicker, substantial handle diameters are usually better(especially for Nikon mount screws), unless the accompanying thicker shaft cannot get past an interfering obstruction or through a access hole. It's good to have a variety of these tools on hand.
Carl's suggestion to match the screwdriver tip to the screw is, of course, the ideal procedure...if you can buy the drivers locally.