We report on individual-InAs nanowire optoelectronic devices which can be tailored to exhibit either negative or positive photoconductivity (NPC or PPC). The NPC photoresponse time and magnitude is found to be highly tunable by varying the nanowire diameter under controlled growth conditions. Using hysteresis characterization, we decouple the observed photoexcitation-induced hot electron trapping from conventional electric field-induced trapping to gain a fundamental insight into the interface trap states responsible for NPC. Furthermore, we demonstrate surface passivation without chemical etching which both enhances the field-effect mobility of the nanowires by approximately an order of magnitude and effectively eliminates the hot carrier trapping found to be responsible for NPC, thus restoring an "intrinsic" positive photoresponse. This opens pathways toward engineering semiconductor nanowires for novel optical-memory and photodetector applications.