I must admit, having had the problem of trying to get "Tiny" screws a few times over the last little while, when ever I am about to throw away some cheap plastic thing, I take the screws out of it and put them in a Jar... there is still never the right size in there when I want one though...:lol
Last time I wanted a small one like you describe, I went to the Poundshop and went round looking at the childrens toys, and stuff like that, looking for anything with small screws in, in my case the ones that held the battery box shut was ideal, and bought one of those as a donor..