Do you have a photo of the island?
Short runways include Skiathos and Mykonos, which are both very busy from May-Sept, and see many charter flights from the UK, Germany, Italy, Scandinavia and other European Countries.
Smaller Greek Islands and some others not so small, that have seasonal direct charter flights popular from Scandinavia are Karpathos, Sitia (Crete), Lemnos, Samos, Mytilene
Preveza (Lefkada), Kavala and Kalamata (Mainland)
Paros (very short runway) was served by Smartwings 737 (Czech airline).