Thanks for posting this Jim. I already had a small screwdriver with a wooden handle which came with my oboe, which Iike but of thes ones you posted a picture of came with my Lorée cor anglais. It has always annoyed me because the end of the handle moves - it never occurred to me to unscrew it completely and look inside!
Howarths do a useful-looking screwdriver-
I'm definitely going to get one of these to keep in my case for running repairs.