I've never touched the wedge screw on any of my BP revolvers. I just press the wedge out from the right side, then continue to withdraw the wedge until the spring hooks on to the screw head as intended. If you want to completely remove the wedge you can just sort of lift up on the wedge to compress the spring, then unhook it from the screw head.
The wedge screw was never really meant to removed on a routine basis. Its only purpose is for the screw head to slightly overlap the wedge slot so as to provide a "lip" on which the wedge spring hooks to retain the wedge and hopefully prevent its loss. When the wedge slot is broached during the machining of the barrel lug, the broaching operation, by it's very nature, makes it impossible to leave the slot with a lip to catch the spring. Hence the wedge screw.