The Major is apparently just what he appears to be: a character with the Hemingway attitude towards his own injury. I thought he might have been derived from a person who had appeared in one of Hemingway's newspaper articles, but couldn't find any mention of such a story.
I wonder why you tagged your question with "science". If it was deliberate, were you asking about the Major's medical condition or his emotional state, or something else.
If we are to believe his doctor, the Major's injury did not destroy structures that could not be healed at that time, WW I. So he could have recovered some use of his hand, but would probably never fence again. Then again, the doctor might well have been decieving him; the tone of the story is ambiguous.
His emotional state, due to his partially disabling wound, the loss of his fencing prowess, or the death of his wife, is probably what you would expect from Hemingway at the time he wrote the story, which you will find discussed by abler critics than me.
The reference can lead you to much more discussion.