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It's certainly possible, but if Kissy is a diminutive of any Japanese word it seems more likely that it would derive from the common word "kisu," a loanword from English "kiss."

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There are various female Japanese names which begin with Kis-, including Kisa, Kisae, Kisako, Kisaki, Kisara and others. It's possible that a bearer of one of these names might go by Kissy in an English-speaking context.