Crafty, last-minute student a buzzer-beater? (10)

I believe the answer is:

flyswatter

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'student a buzzer-beater?' is the definition.
I can't judge whether this defines the answer.

'crafty last-minute' is the wordplay.
'crafty' becomes 'fly' (fly can mean shrewd or crafty).
'last minute' becomes 'swatter' (I can't explain this - if you can you should believe this answer much more).
'fly'+'swatter'='FLYSWATTER'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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