See also Apostrophes in contractions: shan't, sha'n't or sha'nt?.
I was looking into the example of sha'n't because I just ran across that spelling in Henry James's short story, "The Great Condition" (1900), where characters named Bertram Braddle and Henry Chilver converse as follows:
"A-ah!" Chilver murmered, as if only only now with a full view. "She means she'll speak when you are married."
"When we are. And then only on one great condition."
"Well, that if after six months I still want it very much. She argues, you know, that I sha'n't want it."
"You won't then—you won't!"cried Chilver with a laugh at the odd word and passing his arm into his friend's to make him walk again.
There are several striking things about this occurrence of sha'n't. First, in the many stories that James wrote between 1892 and 1900, the spelling with two apostrophes occurs only this once (I believe). Notably, James doesn't spell won't with two apostrophes one line later—and more to the point, he spelled shan't with one apostrophe earlier in the same story:
"Shan't I go with you to the station?" his companion [Chilver] asked.
And finally, Chilver is particularly struck by "the odd word," though he himself used shan't earlier. This suggests that James is using the double punctuation to indicate an unusual pronunciation of the word sha'n't (perhaps as two syllables: sha-ent?), much as he uses a hyphen to indicate an unusual pronunciation or drawing out of "A-ah!" at the beginning of the quoted dialogue.
In any event, it's clear that writers can and do sometimes use two apostrophes in a single contraction, just as they can and sometimes do compress multiple words into one (as in the case of whadya for "what do you") without using any punctuation to clarify what's going on.