First, kudos to you for volunteering to give someone who can't run the experience of an event. That is awesome.
With regards to preping, since you are not able to use your arms (and yes, it is amazing how much swinging your arms actually helps you run), all of your strength is going to have to come from your legs. Aside from just getting your miles in to build up the endurance to run a 10K, you will benefit tremendously by doing hill repeats. You don't have to do it every day - once a week is enough. Find a hill that is at least a half mile long and has maybe a 4% incline (think of it as a 4 foot height change over 100 feet of distance) - do a mile or so to warm up first and then hit the hill as hard as you can, at the top turn around and recover while jogging back to the bottom of the hill, then hit it hard again. You can decide how many repeats is enough for you, maybe adding one or two every week. Be sure to take a slow jog afterwards to cool down and work on getting the lactic acid out of your legs.
If you can't find a suitable hill, I have found that parking structures do very nicely... even tougher actually!
Obviously, if you have a chance to run with the chair (and someone in it), that will also help you train.
Best of luck - you are doing a good thing. Let us know how it works out!
-bill