Green’s Dictionary of Slang

(US) to move stealthily.

1912		Kenna Record (Roosevelt Vo., NM) 4 Oct. 3/4: The yellow man [...] cat-footed noiseless, as he conducted them up a hallway.
1916		H.L. Wilson Somewhere in Red Gap 63: Kind of like him Wilbur was, talking subdued and cat-footing round very solemn.
1924		D. Hammett ‘Death on Pine Street’ in Nightmare Town (2001) 210: A burglar, I thought, an’ cat-footed it down there.
1934		O. Strange Sudden 214: ‘Luck is shore runnin’ my way,’ he commented softly, and cat-footed it to the front door.
1948		N. Nye Breed of the Chaparral (1949) 123: Gun loaded and ready, Tune was cocked to go catfooting down the dim hall.
1959		D. Niland Big Smoke 37: She catfooted slowly into the room.
1961		C. Himes Pinktoes (1989) 15: The white cat [...] started catfooting obliquely toward the northern curb.