Unfortunately, we have not been able to track any public transport services to Skypark, though there are several aspirational web pages for the Exeter Growth Point but no plans or real money for such services.
You could try going to Exeter Airport and walking but the only bus shown on the airport website that includes East Devon is the 56 from Exmouth via Woodbury, timetable here
Click to access Timetable_29921_56,%2056A,%2056B.pdf
For those travelling from the east of the district (Seaton, Colyton) you might want to book a night at the Exeter Airport Hilton before or after your appointment.
Sidmouth Independent News 
You need to look harder Sid.
Stagecoach operate buses from Axminster via Honiton, Ottery and Whimple and stop in between Cranbrook and Clyst Honiton at what will be the main entrance to Skypark runnning roughly every hour during the day. See http://www.stagecoachbus.com/PdfUploads/Timetable_43238_4-4A-4B%20(replacing%2060-380%20services).pdf