Very small chap is old American fighter (9)
I believe the answer is:
Here is my best explanation:
'old american fighter' is the definition.
'very small chap' is the wordplay.
'very small' becomes 'minute' (I've seen this before).
'chap' becomes 'man' (I've seen this before).
'is' is the link.
(Other definitions for minuteman that I've seen before include "Someone always ready for action", "Former American militia member", "early American fighter", "One ready to serve", "American revolutionary militia member", "could be called up at short notice", "ICBM" and "one formed up in Lexington".)