Your motor case is the Mk43, which is the older pre-Vietnam era motor. It looks like parts for it were made in the 55 to 58 timeframe. It is also the older design motor due to the screw in adaptor at the warhead end. It is most likely Navy or Marine Corps due to the gray color. Newer manufactured Mk43 motors have a unitized bulkhead at the warhead end (All aluminum one piece).
You can get the fins/nozzle section out by removing the square aluminum wire that is holding them in place. Look near the back end of the motor for a small slot cut through the side. You can see the wire through that hole. Hold onto the motor body and rotate the fin section. The wire will rotate with the fins. When you see a gap in the wire, stop rotating. Get something small and pointed, like an ice pick or awl, and push it into the gap and try to work it under the square end of the wire so you can pry it up towards you. As you pry it, rotate the fins and wire towards the tool, so that your rotation pushes the wire up out of the hole. once you get the end of the wire above the outer surface of the motor body, continue to rotate the fin section, and it will keep pushing the wire out until it pops out all the way. Now just grab the fin section and work it back and forth. It has a neoprene O-ring around it to seal the gas, so the o-ring will give some resistance, but just keep pulling on it and it will work out eventually. You can also pour some rubbing alcohol into the joint to lube up the o-ring against the aluminum motor body.
Once you get the fin section free, you can use some penetrating oil on the center pin. It should move freely forward and backwards through the hole. The firing wire actually goes through the middle of the pin and runs up to the front of the motor. The center pin is pushed to the rear upon firing, and pushes the fins out, once they are free of the launcher. The locknut will unscrew from the pin, and the star plate will come off and you can remove the pin by pushing it towards the inside of the motor. It might take a while to free the pin up so it moves.
The single powder grain for these motors was around 33 to 35% nitroglycerin. It would burn for about 2-1/2 seconds to get to full speed. It was also quite dangerous because it would detonate high order like a giant stick of dynamite if initiated properly.