In a Manga a character says:
I guess it is a contraction of しない because of the phrase ゾッとしない - pretty disgusting. But (1) I am not completely sure and (2) how does the contraction "work" here in detail?
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ぞっとしない is a set phrase that originally means "not so thrilling" or "unexciting", but it's becoming an obsolete phrase. Few people in the younger generation understand the original meaning of this word correctly. See this page. Technically speaking, "disgusting" is incorrect, but the majority of real examples of ぞっとしない I found from BCCWJ and 小説家になろう actually seem to mean "disgusting" rather than "uninteresting". I suppose future dictionaries will include this new sense.
By the way, if we accept the new sense, ぞっとする and ぞっとしない would effectively mean the same thing. We may include this pair in this list.