The pp is good info, but also check with the event organizers to see if any charter bus service is being provided. If there are any competitions scheduled at DHS, they might have charter buses running between DHS and EWWS, which would save you one transfer, and also probably run more frequently than the Disney bus.
The Disney buses to EWWS run only every half hour, which, combined with the SOG shuttle running once an hour, could make for a very long trip if the schedules don't match up. In fact, unless you're close to the departure time for a DHS shuttle, it might even be faster to walk to the Poly or take the SOG shuttle to TTC (every 20 minutes), monorail to MK, and catch the bus from there to any All Star Resort, where you can catch the EWWS shuttle or preferably a charter bus if available.