I don’t think there’s any connection to be found there.
Aluminum is strong but lightweight, which makes it a common material for things like canes and crutches.
John had a cane in A Study in Pink as part of an elaborate reference to the original stories.
That was completely unrelated to “the singular affair of the aluminum crutch,” which was mentioned in The Musgrave Ritual. The original stories never explained exactly what the The Aluminum Crutch case involved, and the Sherlock team didn’t know what their version would be until it was time to write it up for John’s blog prior to the airing of Series 2.