The Murderess by Alexandros Papadiamantis (1903) — The most celebrated novel by Skiathos's own writer, set on the island in the late 19th century. It follows an old woman who begins killing female infants to spare them the misery of womanhood — a dark, psychologically complex book that reads as anything but sentimental. The island's landscape runs through it like a character. The Nikos Germanis translation into English is the most accessible.
The Gnossiennes and Other Stories by Alexandros Papadiamantis — A collection of his short fiction, which is in many ways more representative of his work than the novel. The stories capture the rhythms of island life — fishing, church, poverty, the seasons — with an attention to detail that makes 19th-century Skiathos feel completely vivid. Worth reading before you arrive.
The Magus by John Fowles (1965) — Not set on Skiathos, but on a different Greek island (loosely based on Spetses). Included here because it captures the particular strangeness of the Aegean islands — the light, the isolation, the sense that rules are suspended — better than almost anything else in English. If you are spending time on a Greek island, this is the book to take.