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The conventional approach of embedding an effective acoustic metric for sound motion in a background flat Minkowski space-time, has recently been extended to incorporate more general curved background metrics, which might contain a black hole. Though the observational aspects of these kinds of acoustics horizons, including the sonic shadow structure and quasi normal modes have received significant attention in the literature, it leaves room for discussions about embedding in more general classes of curved background space-times without optical horizons. Here we propose and study a new class of acoustic metrics that is embedded in a black-bounce space-time, thereby giving a suitable tuneable system to understand possible observational effects of the presence or absence of acoustic horizons. After showing that the metric can represent five types of different effective backgrounds for sound motion, including a novel "acoustic wormhole - optical wormhole" branch, we discuss how the distinctive features of sonic shadows can appear even in the absence of any acoustic horizon due to the wormhole throat present in the acoustic metric.