Hi, Irish and minimac (you did not tell us its name or gender), welcome to the forum and thank you so much for taking in a handicapped bird!
As to its not wanting to come out... Sometimes it has to do more with the set-up than their actual desire to come out and this is especially true of handicapped birds because, although they do not dwell at all on their disabilities and just soldier on with whatever they have left, they do know they are vulnerable and that, some things, are beyond their capabilities. Does the cage have a door that opens down (like the drawbridge over a moat in a castle) and forms like a little platform? Because that is the kind that 'shy' or 'very careful' birds like best but, if it doesn't, you can kind of make one by putting a wire platform right under the bottom of the door to the cage. You will also need both ladders that it can climb down to the floor and branches tied to the side of the cage so he can climb up on its own. Try putting a high value item on the platform right outside his cage (whether it's the actual door to the cage or the one made out of the platform and just wait for the bird to come out on its own. Start by putting the item right next to the cage and, once he starts taking it, start moving the high value item farther from the door so he/she has to walk on the platform to get to it. But, of course, this doesn't work if you free-feed protein food because, when you do, you kind of shoot yourself in the foot when it comes to bribes or rewards...
But the best advice I can give you and the one thing that works all the time is patience... Parrots are not animals that trust from square one (like a puppy would, for example), they observe, analyze and make their own conclusions on which they act upon. Traumatized birds take longer than the 'normal' ones and even the normal ones are slow
One more thing, just because he has only one wing, it doesn't mean that he doesn't need to exercise the other one (this is important for their respiratory system) so don't forget to make him flap fast twice a day for, at least, 5 minutes each time. But, of course, you will need to wait to do this until he feels comfortable enough to come out of his cage and start exploring on its own.