I managed to get a lot of small screws from an optician's shop. Some high street opticians (optometrist, spectacle suppliers, whatever they are called in your part of the world) repair frames and assemble spectacles. One place I visited the repair man was obviously VERY messy and the floor under his bench was covered in literally thousands of screws. They let me scoop up a hand full for free.
Less messy opticians should still be able to supply small screws. Whether they will have the right size, thread and head shape that you require, is obviously a different matter... but might be worth asking.