Basically, what Schwerm has stated. No, you cannot use these weapons effectively against those threats. At 0.2 mm (max limit), your people would be able to wield a spear hardly more than 0.3 mm. By comparison, even a juvenile ant is around 3mm and has 6 legs AND a pair of powerful denticles. An ant bite can send pain waves even in a grown up 6 feet tall human being. How do your people can fare against such a threat when being 1/30 of its length?
To help you think in perspective, would you be able to fight an ant that is double the size of a T-rex? It doesn't need to bite you at all (which would instantaneously clip you in two). Just a stomp by that monster ant would be enough to painfully end your life.
Also keep in mind that arthropods have exoskeletons, so that your weapons would hit the harder parts of the body first, which further implies that you will not be able to punch a hole through your arthropod adversaries (in perspective, a 6 foot person would have to punch a hole in 2 feet thick bone before his spear could hit the softer tissue inside).
So all in all, no. The weapons would be as useless against such adversaries as you trying to bring down a T-Rex with a spear.