Can an undiscovered hex be discovered only by a ship or can it be discovered in any other way?
In the rules:
Discovering with Ships
To discover new land, you must move one of your ships towards the unexplored areas of the board (example 3 A).
If, after moving a ship, one of its ends (bow or stern) points toward the corner (intersection) of an undiscovered hex, you muist discover that hex (example 3 B).
Turn the hex over. If it is a terrain hex, take a number token from the stack whose color/icon matches the color/icon on the back of the terrain hex and place it, number side face up on the hex (example 3 C).
So this implies that this is the only way to diecover new hexes. The shape of the unexplored island is such, that each hex is reachable by sea, there is even a weird "hole" to enable access to the center hex. So I think this is the way the game should be played.