Which character first used the phrase "Shiver me timbers"?
The exact spelling is important here. "Shiver my timbers" was most famously popularized by the archetypal pirate Long John Silver in Robert Louis Stevenson's Treasure Island (1883). Silver used the phrase seven times, as well as its variations such as "shiver my sides", "shiver my soul" and "shake up your timbers". Another pirate, Israel Hands, also uses the phrase at one point. It also appeared in Frederick Marryat's work Jacob Faithful (1835).
Anyway, the writers, who told the stories of pirates, were always grammatically correct, and only the directors and actors of the film adaptions showed the unique style of pirates' speech in an exact way. The famous "me" instead of "my" comes from some British regional accents and is considered one of the key features of pirates' language. It has appeared in popular culture such as with Popeye; in fact, one of the earliest Popeye cartoons from 1934 is even entitled "Shiver Me Timbers!"