What you are looking for is jeweler's screwdrivers. I've got a set I picked up for a few bucks, it's done every small thing I've asked of it.

There are also eyeglass screwdrivers, these are often designed to be easily transportable. I've got one that you can put on a keychain without risking poking a hole in things. It's got both phillips and regular with end caps that screw on over them so it looks like a metal rod a couple of inches long and with a chain on it.