The head is 1.5mm across. I don't have a screwdriver small enough here to take the thing out. I'd recommend popping into a local jewellers. They will have loads of tiny screws. But a competent jeweller will start with a small one and ease it in, knowing which size is too small and realising which size bites well with the current thread. Even one that is fractionally larger than normal will still self tap itself a new thread based on the old one.
They will only charge pennies for it too.
Give that a try.
Also, if you are changing your batteries in the future, put a small neodymium magnet on the neck of your screw driver, and keep one also on your desk, so if the screw pops out unexpectedly, it will be drawn to the magnet.