a) reluctantly
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b) without hesitation
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To do something at the drop of a hat’ means to do it immediately, without delay and at the slightest provocation.
French translation
en un claquement de doigt, au pied levé, en un tournemain
How NOT to translate : *au tomber d’un chapeau
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Examples in the press
‘Marketers must adapt to change, the only certainty for global business this decade
Looking ahead through the 2020s Fundamentally changing marketing methods, modes and models will become normal courses of action. Agencies and marketing departments must diversify hires to capture fresh markets, provide clients and executives with fresh thinking, and reach new audiences with fresh tactics. Marketers will need to be ready to drastically adapt at the drop of a hat or risk becoming obsolete in a futuristic global marketplace.’
Marketing Dive, 14 May 2020
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Everyday usage
I hate to speak in public, but she’ll get up on stage at the drop of a hat.
People will file lawsuits at the drop of a hat these days.
c) joyously
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