(Hand) towel; a cloth or paper used for wiping hands/face — can mean a hand towel, handkerchief, or napkin depending on context.
食事の前に手拭きを渡しますので、手を拭いてください。
I'll give you a hand towel before the meal, so please wipe your hands.
濡れた手を拭くために台所に手拭きを置いておいた。
I left a hand towel in the kitchen to dry wet hands.
外出先で食べた後、紙の手拭きで口元を拭いた。
After eating out I wiped my mouth with a paper napkin.