Very clever, Nick, but you're overthinking it. (I'm no mathematician, I'll say that!)
You do not need the Vigenere cipher--or any other cipher, in fact. It's something different.
However, I will say that your spoiler has the answer in it, amusingly enough.
And, Lord, no, not knowing it without Google does not count as cheating! In fact, you may have to Google that one part in your spoiler to which I referred.
Sorry about how oblique my comments are--I can't say any more without giving it, or at least a huge hint to it, away.
"You do not need the Vigenere cipher"...Thank God for that, lol.
I'm intrigued by the fact that my spoiler appearently has the answer in it without me even realizing it. It's a bit like the following joke, where you in a one-in-a-million chance unintentionally get it right:
Physics teacher: "Billy, what is the derived unit of power?"
Billy (who's been staring out the window half-asleep): "...What?"
Physics teacher: "Correct. Well done, Billy".
But anyway, back to the murder case.
Most of the spoilered text
is about the cipher, so what is there left?
Wait, two other mathematicians are mentioned,
Friedrich Kasiski &
Lewis Carroll. Aside from maths, Kasiski was also an archeologist, but I don't think that's remotely relevant here. Carroll, on the other hand, is the author who wrote Alice in Wonderland. Of course, it would make more sense that a word puzzle would be somehow connected to someone who was a writer. Had no idea he was a mathematician, actually.
Going back to what I said earlier about one person having five letters in their last name, and that there were five clue words in total, I'm inclined to believe that it is Mrs. Wesck based on that. One letter from each of the five words would then be able to form her name. But how?
Just to recap where I'm at, "fax, shops, chips, babbage & rings" ---> W-E-S-C-K, where the arrow would symbolize something related to the text in the spoiler. Perhaps Lewis Carroll, but it could just as well be something else that's so obvious that I'm completely missing it.
Edit: I don't know if my mind is playing tricks on me, but I could have sworn that Horace's friend had six letters in his last name. Oh well, there goes my main suspect, Mrs. Wesck...Could be anyone then, really. :o