Problem was, Ruffo was representative of Ferdinand with full power. Until the king arrived, judges reported to him and he would not have permitted a trial contrary to the surrender condition he had granted (republican captured and judged previous to the surrender were another case).
Moreover, Carracciolo, as other republican leaders, were admirers of the Lumieres of the highest aristocracy. For Ruffo, to have upper-class representatives sentenced to death would have created a complicated situation towards the much troublesome neapolitan populace, which was both the support of the counter-revolution and a major threat for the security of the wealthiest.
Only the arrival of the king could solve the situation. By hanging Carracciollo as a revolutionary (instead of beheading him, as a revolted noble), Hamilton and Nelson took a gage against any twist of mind of Ferdinand.