The crutches are a metaphor for many things. When Nirdlinger has his accident, he's forced to use crutches, and Walter cleverly turns this seeming obstacle into two advantages. First, he employs one of the crutches as the murder weapon to break Nirdlinger's neck. Second, he employs them by using them himself in his impersonation so that it will be remembered that "Nirdlinger" got on the train.
When Nirdlinger has his accident, he's forced to use crutches, and Walter cleverly turns this seeming obstacle into two advantages. First, he employs one of the crutches as the murder weapon to break Nirdlinger's neck. Second, he employs them by using them himself in his impersonation so that it will be remembered that "Nirdlinger" got on the train.