Greens' nose for a toy weapon (3-7)

I believe the answer is:

pea-shooter

I'm a little stuck... Click here to teach me more about this clue!

'toy weapon' is the definition.
'pea shooter' can be an answer for 'toy' (I've seen this before). I'm unsure of the 'weapon' bit.

'greens' nose' is the wordplay.
'greens'' becomes 'pea' (pea green is a kind of green).
'nose' becomes 'shooter' (I can't explain this - if you can you should give a lot more credence to this answer).
'pea'+'shooter'='PEA-SHOOTER'

'for a' acts as a link.

Can you help me to learn more?

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

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