Nice reasoning from smaller case to larger!
Another way to look at it: There are 9 people I asked. The most hands anyone could shake is 8, so the answers I got were 0,1,2,...,7,8
Call the person who shook hands with 8 people A1. He or she shook hands with both members of couples B, C, D, and E. Since they all shook hands with him, the only one left to have shaken hands 0 times is A2.
Then call the person who shook hands with 7 people B1. He shook hands with A1 and with both members of C, D, and E. Since C, D, and E all shook hands with both A1 and B1, that leaves only B2 as the person that shook hands with 1.
Similarly, we find that the couples shook hands with
Since everyone I asked gave a different answer, I obviously didn't ask both E1 and E2, so one of those is me and the other is my wife.