Do fuzzy black caterpillars sting

Monarch caterpillars do not sting. It is a fairly safe assumption that no butterfly or moth larvae possess the capability to inflict a sting via an organ designed for the purpose. As for biting, their mouthparts are designed for the efficient consumption of plant material and are not likely capable of delivering a bite as a defensive mechanism. Of course, there could be rare exceptions. Unusual adaptations in nature are not without precedent.