You will probably have to go with an engineered wood fiber then, or wood chips/mulch that are specifically for playground use (i.e. not so splintery). But you should also keep in mind that with wood, you do have to replenish it, probably on a yearly basis, and so you really should calculate out the cost over time, e.g. five to ten years, because you may find that if you don't have an ongoing budget to access, then you might want to fundraise to get the chopped rubber put in place initially, since you're not going to have to top it off every year.
The Surfacing page on KaBOOM! Accessibility has information on cost, maintenance, safety, etc. of various playground coverings. You may be interested in a turf or rubber tile option.