Now the interesting thing is that won’t and shan’t live side-by-side with wo’n't and sha’n't in these old books. Some quick results on Google Books between 1600 and 1800: 777 won’ts, 57 wo’n'ts; 216 shan’ts, 73 sha’n'ts. Between 1600 and 1700: 48 won’ts, no wo’n'ts; 1 each of shan’t and sha’n't. So it seems it was never the case that the multiple-apostrophe form was more common. For some reason or another, English writers have always preferred a single apostrophe over strict application of “put apostrophes wherever a letter’s missing”.
A look at the text of Sylvie and Bruno Concluded shows that Carroll did in fact use wo'n't where we would use won't; that is, he believed in the same erroneous etymology of this contraction as did Johnson.So - Carroll's "wo'n't" is apparently a contraction of "would not", which made me wonder how he distinguishes it from "woll not". I turned to Dr Johnson's dictionary, to find:
Wo'n't. A contraction of "would not", used for "will not".
It appears, then, that Dr Johnson mistakenly deemed "won't" a contraction for "would not", rather than "woll not", but used in the sense of "will not". Curiouser and curiouser!
It's used in Shirley: A Tale, vol. 1, by Charlotte Brontë. From page 181 of the edition available as a free e-book via Google Books:
Nay: I 've no grand words at my tongue's end, Mr. Moore, but I feel that it wad be a low principle for a reasonable man to starve to death like a dumb cratur': -- I willn't do 't.