Morwen --

Admitedly, when the question first popped into my head I actually looking at a picture, rather than reading a story. In 1806, Thomas Dibdin wrote a Holiday Pantomime about Mother Goose that made her into a witch-figure, complete with magic wand, and raising ghosts. And This roughly contemporary illustration (at least, pre-modern) shows her carrying a cane/crutch (hard to tell from the picture how it's used when she's walking).

And That reminded me of witch at the beginning of The Goose-Girl at the Spring, from Grimms' Children's and Household Tales.

And while she doesn't use a crutch, the witch at the beginning of The Six Swans is identified as a witch because she's old, and has a "bobbing head," which could be a symptom of Parkinson's or some other palsy.