Changing an attack would be a pain. I haven't tried working it 'cause i'm busy with my own map, but- just an idea -you might try giving the hero a second attack in the unit editor that is identical to his primary one, just disabled. Then maybe you could make a trigger that enabled his secondary attack (that could only attack air with whatever other specifics changed) when he picks up the bow, or else disables it when he drops it.
And just to verify (for no particularly important reason, other than i feel like doing so) Acquisition Radius is the range that a unit will begin to automatically attack an enemy. The only time you need to fiddle with that is when your units range is something like 1000 but its acquisition radius is 800. Then it might as well have a range of 800 becaues it will never automatically attack anyone at a range of 1000 (it might work if you ordered the unit to attack, but it's not worth risking

)