How can I minimise damage to a moldy patch of plywood?
A dilute solution of bleach sprayed on it will kill and neutralize the mold. Then wire brush the damaged spot. If you want to prevent this later, seal the plywood with something, primer or polyurethane.

(While bleach contains chlorine which is not good for you, the chlorine is volatile and quickly evaporates. It is typically used by brewers to sterilize equipment for this reason.)