If you say something cattily, you say it in a sharp, unkind way, often as if you are being sweet while you cut someone down. It is the adverb from catty, and it belongs to small, gossipy remarks — a comment on clothes, a smile that is not kind — not to a big open fight. Informal: you would not put it in a serious report. Though actually, English has long used words like this more about women than men, as if only they talk this way. That is an old habit of the language, not a fact about people. Anyone can speak cattily.