Making them more flexible will be down to stretching as apposed to strengthening. Of course,strengthening and then stretching would be optimal.
In a wheelchair or not,Russian twists is a good exercise for core strength. Bingle it. I do these with a 20kg plate held out in front of me.
Proper crunches....not a conventional 'sit-up'. That puts a lot of pressure on the lower back and is more of an isometric contraction,rather than isotonic. Isotonic showing the greatest results for development.
For full development of core strength that is really all you need. You can add in leg raises and side crunches if you wish. Forget anything standing on a ball and balancing! If you strengthen your core properly in the first place,balancing on a ball after that will be cake!
But,is all this really necessary to swing an 8lb gun a few times in succession? Nope. Just by swinging the gun,the body will adapt to that, as it's an exercise in itself,and not just solely for your core. Also back,arms,shoulders and even your legs...why take it beyond what's needed if you don't need to. The body has no interest in being stronger or musclier than it needs to be. Unless of course you want to for other reasons,but then hopefully you wouldn't just be focusing on your core.