1977, Jon Fleming et al., Soldiers on Everest, Her Majesty's Stationery Office, p. 97:
Then he dithered and fannied about.
2007, Philip Bryer, None of Your Business, ISBN 9781847531698, p. 151:
Johnson waited for an age while the barmen tossed bottles back and forth, poured luminous liquids into glasses from great heights, and fannied about with fruit and frivolities.
Obviously, I smirk watching this chaos unfold, from my lofty moral vantage as a woman checking Twitter dozens of times a day, a woman who often presents her husband with meals consisting of fridge remnants as I'm too busy fannying about on the internet to cook or shop.
(chieflyBritain,transitiveandintransitive,idiomatic) To wander about or prowl around.