Scalper makes a good point. It is possible that the wedge has been driven through to the point where the lip on the wedge spring (which is intended to catch on the screw head on the other side of the slot to keep the wedge from falling out completely) has caught on the side of the barrel and is not allowing the wedge to be driven through.
First, tap on the end of the muzzle with a bronze hammer or a piece of wood, like you were trying to drive the barrel back towards the cylinder, as Capt. Aubrey said. This may help loosen the barrel assembly and wedge interface.
Second, tap the wedge further into the slot, which should free the lip of the spring from being caught on the barrel assembly.
Third, tap on the end of the muzzle again, in case the second step tightened up the wedge/barrel interface.
Fourth, and this is the hard part, use a small screwdriver to depress the spring (push down on the spring) while tapping the end of the wedge to drive it out of the slot. This last maneuver may require three hands. I hold the gun between my knees, press down with the screwdriver with my left hand and tap the wedge with a brass or plastic hammer with my right hand. If you need a hand to hold something (like a penny) between the hammer and the wedge, well, I hope you have a friend you can trust to perform one of those operations.