Odd, the main character in Odd and the Frost Giants by Neil Gaiman, is a cane user.
From the publisher:
Odd’s luck has been bad so far. He lost his father on a Viking expedition, his foot was crushed beneath a tree, and the winter seems to be going on forever. But when Odd flees to the woods and releases a trapped bear, his luck begins to change. The eagle, bear and fox he encounters reveal they’re actually Nordic gods, trapped in animal form by the evil Frost Giants who have conquered Asgard, the city of the gods. Can a twelve-year-old boy reclaim Thor’s hammer, outwit the Frost Giants and release the gods?
UK publisher: Bloomsbury (2008)
Author represented by: Merrilee Heifetz of Writers House