Well let's not get tied up in rigid dictations and be legalistic with the "no chatting" deal. You cannot prove that Jesus never spoke a few words to someone before (and we only have but a few of his words & interactions recorded John 21:25), especially like in the instance when he took the little children up in his hands and blessed them (it was probably a loving yet short benediction). He wouldn't have preached a whole sermon to them.
The idle words spoken of mean not "chatting" but rather words spoken off guard, in jest, and other manifestations of ill-spoken words. The Greek word actually means idle in the sense of lazy, and (according to Strong's Lexicon) by implication useless (thus unwholesome), "Let no unwholesome word proceed from your mouth, but only such a word as is good for edification according to the need of the moment, so that it will give grace to those who hear" (Ephesians 4:29). Also in connection with idleness can be seen useless talk, "At the same time they also learn to be idle, as they go around from house to house; and not merely idle, but also gossips and busybodies, talking about things not proper to mention" (1 Timothy 5:13).
That is what it means by "idle" talk. I understand your point about not wanting to be imprecise or to the point when sharing the Gospel but this doesn't mean we shouldn't chat to people! I say 'hi' to people and try to show momentary words of courtesy all the time out of the kindness of my heart, like when I'm in the drive-through, when opening a door for someone, when answering the phone and talking before I hand it to the person they called for (if it wasn't for me), etc. Do you see my distinction? I think I gave the Biblical intention for 'idle' above quite well.
God Bless,
~Josh