Just my thoughts and I really admire you and your efforts btw,
Take a look at outdoor or jogging prams for some inspiration, simple triangular tublar frame design, maybe use bigger rear wheels 26" mountain bike wheel should be fairly cheap to source and durable, you can get 26x1.0-1-5 high PSI (100) slick puncture resistant tyres from many bike tyre manufacturers (continential do a particluary good one) who may be interested in your charity effort.
The more the "cog" is toward the rear of the chair the eaiser it is to lift the front and manoevuer, obviously this requires a level of balance and expertise from the user to learn and get right.
Will they need purchase rings attached to the wheels rims to push the chair, I assume the main reason for these rings is to stop picking up debris & dirt from the road via the tyres but not sure how much they actually add to the controlability, weight etc. Otherwise you'll be suppling a pair of gloves with every chair in fact not necessarily sure having the rings reduces this requirement given the impact on the hands anyway.
Smaller optionally fixed or turning pivot 16" or 20" BMX front wheel to give manoeveurbility when required
They also know how to make these things collaspable.
example here
http://www.babyjogger.com/joggers_strollers.aspx